Question

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

Answer 1

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))`