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

1 Answer
Jul 1, 2016

Answer:

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))#