InterviewSolution
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InterviewSolution
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Show that the points `A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7)` are collinear, and find the ratio in which B divides AC. |
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Answer» The given point are `A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7)`. Therefore, `vec(AB) = (5-1)hati + (0+2)hatj + (-2 + 8)hatk` `" " = 4hati + 2hatj + 6hatk` `vec(BC) = (11 -5)hati + (3-0)hatj + (7+2)hatk` `= 6hati + 3hatj + 9hatk` `vec(AC) = (11-1)hati + (3+1)hatj + (7+8)hatk` `" " = 10hati + 5hatj + 15hatk` `" "|vec(AB)| = sqrt(4^(2) + 2^(2) + 6^(2))= sqrt(16 + 4+ 36)` `" " = sqrt(56) = 2 sqrt(14)` `|vec(BC)| = sqrt(6^(2)+3^(2)+9^(2)) = sqrt(36 + 9 + 81)` `" "= sqrt(126) = 3sqrt(14)` `" "|vec(AC)| = sqrt(10^(2) + 5^(2) + 15^(2)) = sqrt(100 + 25 + 225)` `" " = sqrt(350) = 5sqrt(14)` `therefore " "|vec(AC)| = |vec(AB)| + |vec(BC)|` Thus, the given points A, B, and C are collinear, Also `2 |vec(BC)| = 3|vec(AB)|` Hence, point B divides AC in the ratio `2:3`. |
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