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Vector Algebra

Question
CBSEENMA12036202
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The values of a, for which the points A, B, C with position vectors 2 straight i with hat on top minus straight j with hat on top plus straight k with hat on top comma space straight i with hat on top minus 3 straight j with hat on top minus 5 straight k with hat on top space and space straight a straight i with hat on top minus 3 straight j with hat on top plus straight k with hat on toprespectively are the vertices of a right-angled triangle with C =π/2  are

  • 2 and 1

  • −2 and −1

  • −2 and 1

  • 2 and −1

Solution

A.

2 and 1

BA with rightwards arrow on top space equals straight i with hat on top minus 2 straight j with hat on top plus 6 straight k with hat on top CA with rightwards arrow on top space equals space left parenthesis 2 minus straight a right parenthesis straight i with hat on top space plus 2 straight j with hat on top CB with rightwards arrow on top space equals space left parenthesis 1 minus straight a right parenthesis straight i with hat on top minus 6 straight k with hat on top CA with rightwards arrow on top. CB with rightwards arrow on top space equals space 0 rightwards double arrow space left parenthesis 2 minus straight a right parenthesis space left parenthesis 1 minus straight a right parenthesis space equals 0 rightwards double arrow space straight a space equals space 2 comma 1

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