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| 1. |
If the points `A(1, 0, -6), B(3, p, q) and C(5, 9, 6)` are collinear,find the value of `p and q`. |
| Answer» Given points:`A(1,0,-6)``B(3,p,q)``C(5,9,6)``vecA = overset(^^)(i) - 6overset(^^)(k) ``vecB = 3overset(^^)(i) +poverset(^^)(j) + qoverset(^^)(k)``vecC = 5overset(^^)(i) + 9overset(^^)(j) + 6overset(^^)(k)``vec(AB) = vecB - vecA = 2overset(^^)(i) + poverset(^^)(j) + 15overset(^^)(k)``vec(AC) = vecC - vecA = 4overset(^^)(i) + 9overset(^^)(j) + 12overset(^^)(k)``vec(AB) = lambda*vec(AC)``2overset(^^)(i) + poverset(^^)(j) + 15overset(^^)(k) = lambda*(4overset(^^)(i) + 9overset(^^)(j) + 12overset(^^)(k))`Comparing coefficients:`overset(^^)(i) : 2 = 4lambda rArr lambda = 1/2``overset(^^)(j): p = 9lambda rArr p = 9/2``overset(^^)(k): q+6 = 12lambda rArr q + 6 = 6 rArr q = 0` | |