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The vector from origion to the point A a...

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.

A

`(5sqrt(17))/2 sq.unit`

B

`(5sqrt(15))/3 sq.unit`

C

`(3sqrt(17))/2 sq.unit`

D

None

Text Solution

Verified by Experts

The correct Answer is:
A
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)`
`rArr |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))/2 sq.unit`
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