Two adjacent sides of a parallelogram are respectively by the two vectors `hat(i)+2hat(j)+3hat(k)` and `3hat(i)-2hat(j)+hat(k)`. What is the area of parallelogram?

Options

A. 8
B. `8sqrt(3)`
C. `3sqrt(8)`
D. 192

Answer

B

Explanation

Area of a parallelogram `= vec(A)xxvec(B)`
`=(hat(i)+2hAT(j)+3hat(k))xx(3hat(i)-2hat(j)+hat(k))`
`= | (hat(i),hat(j),hat(k)),(1,2,3),(3,-2,1)|=(8)hat(i)+(8)hat(j)-(8)hat(k)`
Magnitude `=sqrt(64+64+64)=8sqrt(3)`