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The value of a, for which the points A, B and C with position vectors 2hati-hatj+hatk, hati-3hatj-5hatk and a hati-3hatj+hatk respectively are the vertices of a right angled triangle with C=(pi)/(2) are |
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Answer» `-2 and -1` Now, `AC = (ahati- 3hatj + hatk) - (2hati - hatj + hatk) = (a-2)hati - 2hatj` and `BC = (ahati - 3hatj +hatk) - (hati - 3hatj - 5hatk) = (a-1)hati + 6hatk` Since, the `DeltaABC`is rightangledat C, therefore `AC.BC = 0` `rArr {(a-2)hati- 2hatj}.{(a-1)hati + 6hatk} = 0` `rArr (a-2)(a-1)= 0` `:. a = 1` and `2` |
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