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If the vectors hat(i)-3hat(j)+2hat(k), -...

If the vectors `hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j)` represent the diagonals of a parallelogram, then its area will be

A

`sqrt(21)`

B

`sqrt(21)/2`

C

`2sqrt(21)`

D

`sqrt(21)/4`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `a=hati-3hatj+2hatk, b=-hati+2hatj`
Now, `axxb=|{:(hati,hatj,hatk),(1,-3,2),(-1,2,0):}|=-4hati-2hatj-hatk`
`:." "` Area of parallelogram `=1/2|axxb|=1/2sqrt(16+4+1)=sqrt(21)/2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -( MHT CET Corner)
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