What is the angle which the vector `(hat(i)+hat(j)+sqrt(2)hat(k))` makes with the z-axis ?

Options

A. `(pi)/(4)`
B. `(pi)/(3)`
C. `(pi)/(6)`
D. `(2pi)/(3)`

Answer

A

Explanation

`vec(a)=(hat(i)+hat(j)+sqrt(2)hat(k))rArr|vec(a)|=sqrt(1^(2)+1^(2)+(sqrt(2))^(2))=sqrt(4)=2`.
Direction ratios of `vec(a)` are 1, 1, `sqrt(2)`.
Direction cosines of `vec(a)` are `(1)/(2), (1)/(2), (sqrt(2))/(2), i.e., (1)/(2), (1)/(2), (1)/(sqrt(2))`.
`:. cos lambda=(1)/(sqrt(2))rArr lambda=(pi)/(4)`.