determine or find out the direction cosines and

Question

Determine or find out the direction cosines and direction angles for a = (2, 1, -4)

Solution

We will require the magnitude of the vector.

||a|| = √ (4+1+16) = √ (21)

After that the direction cosines and angles are,

cos α = 2/√21         α = 1.119 radians = 64.123 degrees

cos β = 1/√21         β = 1.351 radians = 77.396 degrees 

cos γ = -4/√21         γ = 2.632 radians = 150.794 degrees