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The value of a, for which the points A, ...

The value of a, for which the points A, B, C with position vectors `2hat(i)-hat(j)+hat(k), hat(i)-3hat(j)-5hat(k) and ahat(i)-3hat(j)+hat(k)` respectively are the vertices of a right angled triangles with `C=(pi)/(2)` are

A

2 and 1

B

`-2 and -1`

C

` -2 and 1`

D

` 2 and -1`

Text Solution

Verified by Experts

The correct Answer is:
A
we have,
` vec(AB) = - hati + 2hatj -6hatk, vec(BC) = ( a-1) hati + 6hatk`
` and vec(CA) = (2 -a) hati + 2hatj`
It is given that `triangle ABC` is right angled at C.
` vec(CA) .vec(CA) =0`
` Rightarrow (( 1-a) hati -6hatk) .((2-a) hati + 2hatj) =0`
` Rightarrow ( 1-a) ( 2-a) =0 Rightarrow a=1,2`
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