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If 2veca, 3vecb,2(veca xx vecb) are posi...

If `2veca, 3vecb,2(veca xx vecb)` are position vectors of the vectors A,B,C, of `triangleABC` and `|veca|=|vecb|=1,vec(OA).vec(OB)=-3` (where O is the origin), then

A

Triangle ABC is right-angled triangle

B

Angle B is `90^(@)`

C

`A=cos^(-1)(sqrt(7/19))`

D

The position vector of orthocenter is `2(veca xx vecb)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`vec(OA).vec(OB)=-3`
`rArr 2.3costheta=-3`
`rArr costheta=-1/2 rArr costheta=(2pi)/(3)`
`=4|veca||vecb|^(2)sin^(2)theta+6veca.vecb=4.3/4-61/2=0`
Angle C is `90^(@)`.
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