The vector from origion to the point A and B are `vec(A)=3hat(i)-6hat(j)+2hat(k)` and `vec(B)=2hat(i)+hat(j)-2hat(k)`,respectively. Find the area of the triangle OAB.

Options

A. `5/2sqrt(17) sq.unit`
B. `2/5sqrt(17)sq.unit`
C. `3/5sqrt(17)sq.unit`
D. `5/3sqrt(17)sq.unit`

Answer

A

Explanation

Given `vec(OA)= vec(a)= 3hat(i)-6hat(j)+2hat(k)` and `vec(OB)= vec(b)= 2hat(i)+hat(j)-2hat(k)`
`:. (vec(a)xxvec(b))=|(hat(i),hat(j),hat(k)),(3,-6,2),(2,1,-2)|`
`=(12-2)hat(i)+(4+6)hat(j)+(3+12)hat(k)`
`=10hat(i)+10hat(j)+15hat(k)implies |vec(a)xxvec(b)|`
`=sqrt(10^(2)+10^(2)+15^(2))`
`=sqrt(425)=5sqrt(17)`
Area of `DeltaOAB=1/2|vec(a)xxvec(b)|=(5sqrt(17))/2sq`.unit.