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

Options

A. 5
B. 1
C. 6
D. 8

Answer

C

Explanation

Let the position vectors of the points A,B,C are `vec0, veca+vecb,veca-vecb and theta =90^(@)`
`:.` Area of triangle `=(1)/(2)|vec(AB)xx vec(AC)|`
`=(1)/(2)| (veca+vecb)xx(veca -vecb)|`
`=(1)/(2)| 2 vecb xx veca|`
`=|vecb||veca|sin theta`
`=3xx2 sin 90^(@)`
`=6`