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If |vec(a)|=2,|vec(b)|=3andvec(a),vec(b)...

If `|vec(a)|=2,|vec(b)|=3andvec(a),vec(b)` are mutually perpendicular, then the area of the triangle whose vertices are `vec(0),vec(a)+vec(b),vec(a)-vec(b)` is

A

5

B

1

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Let position vectors of the poits A, B C are `0, a+b, a-b` respectively and `theta=90^@`
`:." "` Area of triangle `=1/2|(a+b)xx(a-b)|`
`=1/2|(a+b)xx(a-b)|`
`=1/2|2bxxa|`
`=|b|a|sin theta=3xx2sin 90^@=6`
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