If the projection of the vector a on b is `|axxb|` and if `3b=hati+hatj+hatk`, then the angle between a and b is

Options

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

Answer

A

Explanation

Given ,projection of `a on b=|axxb|`
`rArr (a.b)/(|b|)=|axxb|`
`rArr (|a||b|costheta)/(|b|)=|a||b|sintheta`
`rArr tan theta=(1)/(|b|)`
`rArr tan theta= (1)/((1)/(3)sqrt(1^2+1^2+1^2))`
`rArr tan theta = sqrt(3)`
`rArr theta=(pi)/(3)` .