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The values of a, for which points A, B, C with position vectors 2î-ĵ+k̂, î-3ĵ-5k̂ and aî-3ĵ+k̂ respectively are the vertices of a right angled triangle with C=π/2 are

1. 2 and 1
2. −2 and −1
3. −2 and 1
4. 2 and −1

Correct answer: 2 and 1

Solution

CA = A-C = (2-a, 2, 0) and CB = B-C = (1-a, 0, -6). For angle C = 90 deg, CA.CB = (2-a)(1-a) = 0, so a = 2 or a = 1. Answer: 2 and 1.

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