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The vectors from origin to the points A ...

The vectors from origin to the points A and B are `vecA=3hati-6hatj+2hatk` and `vecB=2hati+hatj+2hatk` respectively. The are of triangle `OAB` be

A

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

B

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

C

`(3)/(5)sqrt(17)` sq. units

D

`(5)/(3)sqrt(17)` sq. units

Text Solution

Verified by Experts

The correct Answer is:
A
Given `vec(OA)=veca=3hati-6hatj+2hatk` and `vec(OB)=vecb=2hati+hatj-2hatk`
`(vecaxxvecb)={:|(hati,hatj,hatk),(3,-2,1):}|`
`=(12-2)hati+(4+6)hatj+(3+12)hatk`
`=10hati+10hatj+15hatkimplies|vecaxxvecb|=sqrt(10^(2)+10^(2)+15^(2))`
`=sqrt(425)=5sqrt(17)`
Area of `triangleOAB=(1)/(2)|vecaxxvecb|=(5sqrt(17))/(2)` sq. units sq.
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