Question

If `|vec(a)| = 2, |vec(b)|= 7 and (vec(a) xx vec(b))=(3 hat(i) + 2 hat(j) + 6 hat(k)), " find the angle between " vec(a) and vec(b).`

Answer 1

Correct Answer - `pi/6`
`vec(a) xx vec(b)= (3 hat(i) + 2 hat(j)+ 6 hat(k))`
`rArr|vec(a) xxvec(b)|= sqrt(3^(2)+2^(2)+6^(2))=7 rArr|vec(a)||vec(b)| sin theta = 7`
`rArr sin theta= 7/(|vec(a)||vec(b)|)=7/((2 xx7))=1/2 rArr theta = 30^(@).`