If `vec(a) = (3hat(i)+hat(j)-4hat(k)) and hat(b)= (6hat(i) + 5 hat(j) ,2 hat(k))`, ` " find " (veca xx vec(b)) and |vec(a) xx vec(b)|`.

Explanation

We have `(vec(a) xx vec(b))= |(hat(i), hat(j),hat(k)),(3,1,-4),(6,5,-2)|`
`=(-2 + 20) hat(i) - (-6 + 24) hat (j) + ( 15-6) hat(k)`
`=(18 hat(i) - 18 hat(j) + 9 hat(k))`
`|vec(a) xx vec(b)|^(2)= {(18)^(2) + (-18)^(2) + 9^(2)}=729`
` rArr |vec(a) xx vec(b)|= sqrt(729)= 27.`