2-D Vectors

Key Questions

• What is the definition of a vector?

  A quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of which is proportional to the magnitude.

  

  Konstantinos Michailidis · 1 · Apr 22 2018
• How do I find the resultant of vectors?

  Resultant of vectors can be found using the law of cosines.

  If A and B are two vectors with an angle between them equal to #theta# (#theta < pi#), their resultant R is given by,

  #R = [A^2 + B^2 + 2AB Cos theta]^(1/2)#, this gives the magnitude of R.

  If the vector R makes an angle #alpha# with vector A, then

  #alpha = arctan [(B Cos theta)/(A + B Sin theta)]#

  Aritra G. · 1 · May 30 2015

• How do I find the magnitude of a vector?
• How do I find the resultant of vectors?
• How can vectors be parallel?
• What is meant by the initial point of a vector?
• What is the definition of a vector?
• How do I multiply a vector by a scalar?
• What are common mistakes students make with 2-D vectors?
• What is the terminal point of a vector?
• How do you find the magnitude and direction for U: magnitude 140, bearing 160° V: magnitude 200, bearing 290°?
• How do you write vector U = 6 and Theta = 45 degrees in cartesian form?
• How do you find the scalar and vector projections of b onto a given #a = <3, -6, 2>#, #b = <1, 1, 1>#?
• How do you find the scalar and vector projections of b onto a given #a = i + j + k#, #b = i - j + k#?
• How do you find the scalar and vector projections of b onto a given #a = ‹3, 2, 1›#, #b = ‹0, 1, 3›#?
• How do you write the vector equation that passes through point (5,7) and parallel to <2,0>?
• How do you write the vector equation that passes through point (-1,4) and parallel to <6,-10>?
• How do you write the vector equation that passes through point (-6,10) and parallel to <3,2>?
• How do you write the vector equation that passes through point (1,5) and parallel to <-7,2>?
• How do you write the vector equation that passes through point (1,0) and parallel to <-2,-4>?
• How do you write the vector equation that passes through point (3,-5) and parallel to <-2,5>?
• Are the vectors #u=<1, -2># and #v=<4, 8># parallel, orthogonal, or neither?
• Show that the vectors # 4 bb ul a - 8bb ul b# and #-26bb ul a+52bb ul b # are parallel?
• Let #veca=<−2,3># and #vecb =<−5,k>#. Find #k# so that #veca# and #vecb# will be orthogonal. Find k so that →a and →b will be orthogonal?
• Vectors - Span #RR^2#?