Question

If `vec(A)=3hat(i)+hat(j)+2hat(k)` and `vec(B)=2hat(i)-2hat(j)+4hat(k),` then find the value of `|vec(A)xxvec(B)|.`
A. `8sqrt(2)`
B. `8sqrt(3)`
C. `8sqrt(5)`
D. `5sqrt(8)`

Answer 1

Correct Answer - B
`vec(A)xxvec(B)= | (hat(i),hat(j),hat(k)),(3,1,2),(2,-2,4)|`
`=(1xx4-2xx-2)hat(i)+(2xx2-4xx3)hat(j)+(3xx-2-1xx2)hat(k)`
`=8hat(i)-8hat(j)-8hat(k)`
Mangnitude of `vec(A)xxvec(B)=|vec(A)xxvec(B)|`
`=sqrt((18)^(2)+(-8)^(2)+(-8)^(2))= 8sqrt(3)`