A vector is given by `vec (A) = 3 hat(i) + 4 hat(j) + 5 hat(k)`. Find the magnitude of `vec(A)` , unit vector along `vec(A)` and angles made by `vec(A)` with coordinate axes.

Explanation

`|vec(A)| = A = sqrt(A_(x)^(2) + A_(y)^(2) + A_(z)^(2))`
` = sqrt((3)^(2) + (4)^(2) + (5)^(2)) = 5 sqrt(2)`
`hat(A) = (vec(A))/(| vec(A)|) = ( 3 hat(i) + 4 hat(j) + 5 hat (k))/( 5 sqrt(2))`
`cos alpha = (A_(x))/(|vec(A)|) = (3)/( 5 sqrt(2)) , alpha = cos ^(-1) ((3)/(5 sqrt(2)))`
`cos beta = (A_(y))/(|vec(A)|) = (4)/(5 sqrt(2)) , beta = cos^(-1) ((4)/(5 sqrt(2)))`
`cos gamma = (A_(z))/(|vec(A)|) = (5)/( 5 sqrt(2)) , gamma = cos ^(-1) ((1)/( sqrt(2))) = (pi)/(4)`
`alpha , beta` and `gamma` angles made by `vec(A)` with `x , y , z` axes, respectively.