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Q.

The values of a, for which the points A, B, C with position vectors 

 2 i - j + k, i - 3 j- 5 k and ai - 3j + k respectively are the vertices of a right angled triangle with C=π2 are

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a

2, –1 
 

b

–2, –1 
 

c

2, 1 
 

d

–2, 1 
 

answer is A.

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Detailed Solution

OA=2i-j+k     OB=i-3j-5k OC=ai-3j+k AC=(a-2)i-2j    BC=(a-i)i+6k AC.BC=0  (a-2)(a-1)=0  a=2,1

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