The values of a , for which the points A , B , C with position vectors 2 i ^ − j ^ + k ^ , i ^ − 3 j ^ − 5 k ^ and a i ^ − 3 j ^ + k ^ respectively are the vertices of a right-angled triangle wi

Question

The values of a , for which the points A , B , C with position vectors 2 i ^ − j ^ ​ + k ^ , i ^ − 3 j ^ ​ − 5 k ^ and a i ^ − 3 j ^ ​ + k ^ respectively are the vertices of a right-angled triangle with C = 2 π ​ are

TestHub · Accepted Answer

⇒ B A = i ^ − 2 j ^ ​ + 6 k ^ C A = ( 2 − a ) i ^ + 2 j ^ ​ CB = ( 1 − a ) i ^ − 6 k ^ C A ⋅ CB = 0 ⇒ ( 2 − a ) ( 1 − a ) = 0 ⇒ a = 2 , 1

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