If `| vec a|=2,\ | vec b|=7\ a n d\ vec axx vec b=3 hat i+2 hat j+6 hat k ,\ ` find the angle between ` vec a\ a n d\ vec bdot`

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

A

Explanation

`|vec(a)|=2,|vec(b)|=7`.
`vec(a)xxvec(b)=3hat(i)+2hat(j)+6hat(k)`
We know, `vec(a)xxvec(b)=|vec(a)||vec(b)|sin theta.hat(n)` where `hat(n)` is unit vector.
`rArr |vec(a)xxvec(b)|=|vec(a)||vec(b)|sin theta`
`rArr |2hat(i)+2hat(j)+6hat(k)|=(2)(7) sin theta`
`rArr sqrt(9+4+36)=(2)(7)sin theta`.
`rArr pm7=(2)(7)sin theta`.
`:. sin theta = pm(1)/(2)`.
`sin theta` is acute angle, `theta=30^(@)`