Find the area a parallelogram whose diagonals are ` vec a=3 hat i+ hat j-2 hat ka n d vec b= hat i-3 hat j+4 hat kdot`

Options

A. `7sqrt(3)` sq units
B. `5sqrt(3)` sq units
C. `3sqrt(5)` sq units
D. none of these

Answer

B

Explanation

`(vec(d_(1))xxvec(d_(2)))=|(hat(i),hat(j),hat(k)),(3,1,-2),(1,-3,4)|=(4-6)hat(i)-(12+2)hat(j)+(-9-1)hat(k)`
`=(-2hat(i)-14hat(j)-10hat(k)) `
`rArr|vec(d_(1))xxvec(d_(2))|=sqrt((-2)^(2)(-14)^(2)+(-10)^(2))=sqrt(300)=10sqrt(3)`
`rArr` area of the ||gm `=(1)/(2)|vec(d_(1))xxvec(d_(2))|=5sqrt(3)` sq units.