Find a vector ` vec r` of magnitude `3sqrt(2)` units which makes an angle of `pi/4` and `pi/2` with `y` and z-axis respectively.

Options

A. `r= pm 3hati+3hatj`
B. `r=3hati+3hatj`
C. `r=pm 3hati+3hatj`
D. None of these

Answer

A

Explanation

Here, `m="cos"pi/4=1/sqrt(2)` and `n="cos"pi/2 =0`
Therefore, `l^(2)+m^(2)+n^(2)=1` [given]
`l^(2)+1/2 +0=1`
`implies l= pm 1/sqrt(2)`
Hence, the required vector `r=3sqrt(2) (l hat(i)+m hat(j)+n hat(k))` is given by `r=3sqrt(2) (pm 1/sqrt(2) hat(i) +1/sqrt(2) hat(j) + 0hat(k))=r= pm 3 hat(i)+3hat(j)`