Unit Vectors

Key Questions

• What is a direction vector?

  The direction of a vector is the direction along which it acts.
  It has a certain magnitude.

  For example, we say 10 N force in the east.
  Here, 10 N is the magnitude and towards the east is the direction.

  The direction is specified using a unit vector.
  Let n be a unit vector along a certain direction and #A# be some scalar, then a vector with magnitude that of #A# and direction that of n is defined as,

  A = #A# n

  Aritra G. · 3 · May 31 2015
• What is a unit vector?

  A unit vector is a vector that has a magnitude(length) of just 1 unit.

  Please see the video example below ...

  Unit Vector Video

  AJ Speller · · Sep 19 2014

• What is a unit vector?
• How do I find the unit vector of a plane?
• How do I calculate a unit vector?
• How do I multiply two unit vectors?
• What are unit vectors used for?
• What is a direction vector?
• What does it mean to normalize a vector?
• How do you find the principal unit normal vector to the curve at the specified value of the parameter #r(t) = cos(3t)i + 2 sin(3t)j + k# where t is pi?
• An airplane has an airspeed of 500 kilometers per hour bearing N45°E. The wind velocity is 60 kilometers per hour in the direction N30°W. Find the resultant vector representing the path of the plane relative to the ground?
• How do you find a unit vector that is orthogonal to a and b where #a = −7 i + 6 j − 8 k# and #b = −5 i + 6 j − 8 k#?
• Given 2 vectors #A = 4.00i + 3.00j # and #B =5.00i - 2.00 j# how do you find the magnitude of each vector?
• Given 2 vectors #bbA = 4bbi + 3bbj # and #bbB =5bbi - 2bbj# how do you write an expression for the vector difference #bbA - bbB# using unit vectors?
• Given 2 vectors #A = 4.00i + 3.00j # and #B =5.00i - 2.00 j# how do you find the magnitude & direction of the vector difference A - B?
• Vector B has x, y, and x components of 5.5, 7.1, and 1.4 units, respectively. How do you calculate the magnitude of vector B?
• A unit vector parallel to vector V= (2,-3,6) is what?
• How do you find a unit vector in the same direction as a=(-10, 6, -7)?
• How do you find a unit vector orthogonal to both #(2,0,1,-4)# and #(2,3,0,1)#?
• How do you find two unit vectors parallel to vector a= [-4, -1, -6]?
• How do you find a unit vector that is orthogonal to both u= - 6i + 4j + k and v= 3i + j + 5k?
• Given #A = i(x+2y) - j(y+3z) +k (3x-y)#, how do you determine a unit vector parallel to #A# at point #P(1,-1,2)#?
• How do you find a unit vector from the point P=(1,1) Q=(5,4)?
• How do you find unit vector perpendicular to plane: 6x-2y+3z+8=0?
• The vector U=2i +3j -2k, how do you find a unit vector parallel to U?
• How do you find a unit vector normal to the plane which passes through the following points (1,1,1),(2,0,2),(1,1,2)?
• How do you find the unit vector of 5i-12j?
• How do you find the unit vector of -4+3i?
• How do you find two unit vectors perpendicular to the xy plane with equation 3x-4y=17?
• How do you find a unit vectors are orthogonal to both i+j and i+k?
• How do you find a unit vector that is perpendicular to both the vector u = 0,2,1 and v = 1, -1, 1?
• How would you find a unit vector in the direction v = 6i-2j?
• How would you find the unit vector having the same direction as v=-10i+24j?
• How would you find the unit vector having the same direction as v = -5i + 12j?
• How would you find the unit vector along the line joining point (2, 4, 4) to point (-3, 2, 2)?
• How would you find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (3, -4, 4), Q = (6, -1, 7), and R = (6, -1, 9)?
• How do you find the unit vector parallel to the resultant of the vectors A= 2i - 6j -3k and B = 4i + 3j- k?
• How do you find the unit vector having the same direction as vector v = 2i - j + k?
• How do you find a unit vector in the direction of v: v=3i-2j?
• How do you find all unit vectors orthogonal to both the vectors given below: (1,2,-1) and (3,3,-4)?
• How do you find a unit vector in the direction of the vector v=(-3,-4)?
• How do you find the unit vector that has the same direction as the vector v=5j?
• How do you find a unit vector that is oppositely directed to v = (1, 3,- 4)?
• How do you find a unit vector of 4i+3j?
• How do you find a unit vector of i-3j?
• How do you find the unit vector in the direction of the vector a = 3i + 4j?
• How do you find two unit vectors orthogonal to both i-j+k and 4j+4k?
• How do you find a unit vector parallel to the xz plane and perpendicular to i - 2j + 3k?
• How would you find a unit vector perpendicular to plane ABC where points are A(3,-1,2), B(1,-1,-3) and C(4,-3,1)?
• How do you find a unit vector that is orthogonal to a and b: a = 7 i − 4 j + 8 k and b = −7 i + 9 j + 4 k?
• How do you find a unit vector which is parallel to the vector which points from (4,13)(19,8)?
• If a= i +6j+k and b= i+13j+k, how do you find a unit vector with positive first coordinate orthogonal to both a and b?
• How do you find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (4, 0, 2), Q = (7, 3, 5), and R = (7, 3, 8)?
• How do you find two unit vectors that make an angle of 60° with v = ‹3, 4›?
• How do you find a unit vector with the same direction as 8i - j + 4k?
• How do you find a unit vector perpendicular to the vectors 6i + 2j - k and -2i + 3j + 4k?
• How do you find a unit vector that is orthogonal to both 2i+2j and 2i+2k where i,j, and k are vector use dot product?
• How do you find the unit vector that has the same direction as the vector v = –12j?
• How do you find a unit vector perpendicular to both vector u(1, -1,-1)and vector v(2, -2, 3)?
• How do you find a vector of length 1 in the same direction as (6,-8)?
• How do you find unit vector of #a=(1, 2, -2)# in direction of #a#?
• How do you find a unit vector u in the same direction as the vector ⟨1,−2,−3⟩?
• If the vector v lies in the first quadrant and makes an angle of 10 degrees with the positive x-axis and |v| = 7, find v in component form?
• How do you find a unit vector in the direction of 3i+4j-k?
• How do you find two unit vectors orthogonal to A=(1, 3, 0) B =(2, 0, 5) first vector must have positive first coordinate?
• How do you find the unit vector in the direction of the vector a = 2i + 3j?
• How do you find the unit vector that is orthogonal to the plane through the points P = (3, -3, 0), Q = (5, -1, 2), and R = (5, -1, 6)?
• How do you find a unit vector that is perpendicular to both #-2i + j + 3k# and #i - j - 2k#?
• How do you find the unit vector that has the same direction as the vector below: v= 4j?
• How do you find the unit vector of v=4i+2j?
• Consider the surface xyz = 45. How do you find the unit normal vector to the surface at the point (3, 5, 3) with positive first coordinate?
• How do you find a unit vector with positive first coordinate that is orthogonal to the plane through the points #P = (3, -3, 0), Q = (5, -1, 2)#, and #R = (5, -1, 6)#?
• How do you find the unit vector for the following vector that connects (2,-5) and (0,3)?
• How do you find a unit vector u that is orthogonal to a and b where a = 7 i - 5 j + k and b = -7 j - 5 k?
• How do you find a unit vector perpendicular to a 3-D plane formed by points (1,01),(0,2,2) and (3,3,0)?
• How do you find a unit vector perpendicular to both (2,1,1) and the x-axis?
• If V= (4,-3), how do you find the direction?
• How do you find the unit vector in the same direction as (-5, 3)?
• How do you find the unit vector that has the same direction as the vector from the point A= (5, 2) to the point B= (3, 2)?
• How do you find the unit vector for v = -6i +5j?
• A vector has a magnitude of 16 and a direction of 120°. How do you write the vector in terms of unit vectors?
• A vector has a magnitude of 12 and a direction of 80°. How do you write the vector in terms of unit vectors?
• How do you find the unit vector in the direction of #vecu = (2,1,-3)#?
• How do you find the unit vector in the direction of v: v=4i-2j?
• How do you find a unit vector from the point P=(1,1) and toward the point Q=(4,5)?
• How do you find a unit vector that has the same direction as the given vector −5i + 9j?
• How do you find a unit vector b perpendicular to another unit normal vector, which is #4/5hati + 2/5hatj - 3/5hatk#?
• How do you find the direction cosines of the vector #u=2i -4j+4k# and find the direction angles?
• If your given the plane #-x+6y+5z=21#. How do you find the normal vector for that plane and a point on that plane?
• How do you find a unit vector in the direction of v: v = - 5i + 2j?
• Consider the surface xyz=30. How do you find the unit normal vector to the surface at (2,5,3)?
• Given two points (4i, -2j, 3k) and (i, j, -3k), how do you find a unit vector parallel to the line segment AB?
• For the given vector: v = 3i - j + 2k, how do you write a unit vector in the direction of vector v?
• What is the unit vector of this vector v = -2i + 5j?
• What is the unit vector of this vector v = 2i - j + k?
• Given U is a vector with an initial point of (6,-4) and a terminal point of (-2, 8). How do you write u as a linear combination of the standard unit vector i and j?
• How do you find the unit vector having the same direction as vector u = i - 6 j + 5 k?
• Let F = 2i - 6j + 10k and G = i+ Gy j + 5k. If F and G have the same unit vector, what is Gy?
• Given that A = i+ a j + k and B = a i+ j + k, if A and B are normal to each other, what is a?
• How do you find a unit vector orthogonal to both vectors (1, -3, 2) and (-1, 2, 3)?
• How do you write vector CD as the sum of unit vectors for points C (7,4) & D (-8, -1)?
• How do you find the unit vectors perpendicular to the plane determined by the three points (1, 3, 5), (3, -1, 2), and (4, 0, 1)?
• How do you find a unit vector perpendicular to 4i - 3j +k and parallel to the x-y plane?
• How do you find the unit vector perpendicular to the vector (4i - 3j)?
• What is the unit vector in the direction of (-3,5,4)?
• How do you find the two unit vectors in R^2 parallel to the line y=3x+4?
• How do you find a Unit vector perpendicular to vector a=(4,-3,1) and vector b=(2,3,-1)?
• How do you find the unit vector having the same direction as vector #a = 8i-15j#?
• Given vector #vecA=2hati + 1hatj# and vector #vecB=3hatj#, how do you find the component of #vecA# in the direction of #vecB#?
• Given vector A=2i + 1j and vector B=3j, how do you find the component of B in the direction of A?
• How do you find a unit vector a) parallel to and b) normal to the graph of f(x)=-(x^2)+5 at given point (3,9)?
• If Vector a= 2i - 4j + k and Vector b= -4i + j +2k how do you find a unit vector perpendicular to both vector a and b?
• How do you find a unit vector that is orthogonal to both u = (1, 0, 1) v = (0, 1, 1)?
• How do you find the unit vectors that are parallel to the tangent line to the curve y = 2sinx at the point (pi/6,1)?
• How do you find a unit vector normal to the surface #x^3+y^3+3xyz=3# ay the point(1,2,-1)?
• How do you find two unit vectors orthogonal to a=⟨−1,2,1⟩ and b=⟨−4,0,−5⟩?
• How do you find a unit vector perpendicular to two vectors that is perpendicular to both the vectors u = (0, 2, 1) and v = (1, -1, 1)?
• How do you find a unit vector (a) parallel to and (b) normal to the graph of f(x) at the indicated points given function: #f(x) = sqrt(25+x^2)# and point: (3,4)?
• How do you find two unit vectors which are orthogonal to the vector 3i-j+2k and parallel to the yz plane?
• How do you find a unit vector a)parallel to and b)normal to the graph of #f(x)# at the indicated point. #f(x)= x^3, "at" (1,1)#?
• How do you find two unit vectors orthogonal to A=(1, 3, 0) B =(2, 0, 5)?
• How do you find the unit vector which bisects the angle AOB given A and B are position vectors a=2i-2j-k and b=3i+4k?
• How do you find the unit vector in the direction of PQ p = (7,-4) q = (-3,2)?
• How do you find all unit vectors orthogonal to v=i+j+k?
• How do you find the unit vector, in the first quadrant, that is parallel to the line tangent to the parabola y = x^2 at the point (4, 16)?
• How do you find the unit vector having the same direction as vector #v = –12j#?
• How do you find the unit vector having the same direction as vector #v = -6i +5j#?
• How do you find two unit vectors that are orthogonal to (-3,4)?
• How do you find all unit vectors normal to the plane which contains the points #(0,1,1),(1,−1,0)#, and #(1,0,2)#?
• How do you find all unit vectors that is orthogonal to the plane through the points P = (3, -3, 0), Q = (5, -1, 2), and R = (5, -1, 6)?
• How do you find the unit vector having the same direction as vector #u=3i-4j#?
• How do you find a vector of length 10 that is oppositely directed to u=3i-4j?
• How do you find the unit vector in the direction of the given vector u=<3,0>?
• How do you find the unit vector in the direction of the given vector u=<-2,2>?
• How do you find the unit vector in the direction of the given vector 6i-2j?
• How do you find the unit vector in the direction of the given vector w=4j?
• Given the initial (-3,1) and terminal (4,5) points of a vector, how do you write a linear combination of the standard unit vector i and j?
• Given the initial #(-1, -5)# and terminal #(2,3)# points of a vector, how do you write a linear combination of the standard unit vector #hati# and #hatj#?
• How do you write the ordered triple that represents TM given T(-2,4,7) and M(-3,5,2)?
• How do you write the ordered triple that represents TM given T(2,5,4) and M(3,1,0)?
• How do you write the ordered triple that represents TM given T(3,-5,6) and M(-1,1,2)?
• How do you write the ordered triple that represents TM given T(-5,8,3) and M(-2,-1,-6)?
• How do you write the ordered triple that represents TM given T(0,6,3) and M(1,4,-3)?
• How do you find the sum of the unit vectors (2,2,7) and (5, -6, 2)?
• How do you find the sum of the unit vectors (-6,1,0) and (-4,5,-1)?
• How do you find the sum of the unit vectors (9,7,-11) and (7,3,-2)?
• How do you find the sum of the unit vectors (12,2,6) and (-8,7,-5)?
• How do you find the sum of the unit vectors (-1,2,-4) and (-8,5,-10)?
• How do you find the sum of the unit vectors #(-9,12,-5)# and #(6,5,-5)#?
• Is #2+-1sqrt3# the same as #2+-sqrt3# ?
• Multiply the vectors. The answer is 29 - j29?