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Let ABC be a triangle, the position vect...

Let ABC be a triangle, the position vectors of whose vertices are respectively `7 hatj + 10 hatk , -hati + 6 hat j + 6 hatk and -4 hati + 9 hatj + 6 hat k . " Then, " Delta ABC ` 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, `vec(AB) = -hati -hatj -4hatk, vec(BC) = -3hati +3hatj and vec(CA) = 4hati -2hatj +4hatk`. Therefore,
`|vec(AB)| = |vec(BC)| = 3sqrt2 and |vec(CA)| = 6`
Clearly, `|vec(AB)|^(2) +|vec(BC)|^(2) = |vec(AC)|^(2)`
Hence, the triangle is right-angled isosceles triangle.
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