Find the directional cosines of vector `(5hati+2hatj+6hatk)`. Also write the value of sum of squares of directional cosines of this vector.

Answer

`(5)/(sqrt(65)), (2)/(sqrt(65)), (6)/(sqrt(65)); 1`

Explanation

Let `alpha, beta & gamma` are the angles of vector `(5hati+2hatj+6hatk)` from x, y and z-axis respectively.
then `cos alpha = (A_x)/(A) = (5)/(|5hati+2hatj+6hatk|)= (5)/(sqrt(65))`
`cos beta =(A_y)/(A) = (2)/(|5hati+2hatj +6hatk|) = (2)/(sqrt(65))`
`cos gamma = (A_z)/(A) = (6)/(|5hati+ 2hatj+6hatk|) = (6)/(sqrt(65))`
The sum of squares of directional cosines of this vector
`cos ^(2) alpha + cos ^(2) beta + cos^(2) gamma = (5^(2) + 2^(2) + 6^(2))/(65) = (65)/(65) = 1`