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If the position vectors of the vertices ...

If the position vectors of the vertices A,B and C of a `DeltaABC` are `7hatj+10k,-hati+6hatj+6hatk and -4hati+9hatj+6hatk`, respectively, the triangle is

A

isosceles

B

equilateral

C

right angled

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
We have, `AB=-hati-hatj-4hatk,BC=-3hati+3hatj`
and `CA=4hati-2hatj+4hatk`.
therefore, `|AB|=|BC|=3sqrt(2) and |CA|=6`.
Clearly, `|AB|^(2)+|BC|^(2)=|AC|^(2)`
Hence, the triangle is right angled isoscels triangle.
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