How do you find the direction cosines and direction angles of the vector?

1 Answer
Jul 1, 2016

If the vector is (x, y, z) and r=|(x, y, z)|, the direction cosines are (x/r, y/r. z/r) and the angles are (cos^(-1)(x/r), cos^(-1)(y/r), cos^(-1)(z/r)).

Explanation:

If the vector is x i+yj+zk=(x, y, z) and

r = length of ( x, y, z ) =sqrt(x^2+y^2+z^2),

the direction cosines are (x/r, y/r. z/r) and the angles are

(cos^(-1) (x/r), cos^(-1) (y/r), cos^(-1) (z/r))

Example: Vector is (1, 1, 1)..

r=sqrt(1+1+1)=sqrt 3.

Direction cosines are

(1/sqrt 3, 1/sqrt 3, 1/sqrt 3).

Angles are

(cos^(-1) (1/sqrt 3), cos^(-1) (1/sqrt 3), cos^(-1)(1/sqrt 3))