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Show that the points A(2, 3, -4), B(1, -2, 3) and C(3, 8, -11) are collinear. |
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Answer» Given - A = (2,3,-4) B = (1,-2,3) C = (3,8,-11) To prove – A, B and C are collinear Formula to be used – If P = (a,b,c) and Q = (a’,b’,c’),then the direction ratios of the line PQ is given by ((a’-a),(b’-b),(c’-c)) The direction ratios of the line AB can be given by ((1-2),(-2-3),(3+4)) =(-1,-5,7) Similarly, the direction ratios of the line BC can be given by ((3-1),(8+2),(-11-3)) =(2,10,-14) Tip – If it is shown that direction ratios of AB=λ times that of BC , where λ is any arbitrary constant, then the condition is sufficient to conclude that points A, B and C will be collinear. So, d.r. of AB =(-1,-5,7) =(-1/2) Χ (2,10,-14) =(-1/2) Х d.r. of BC Hence, A, B and C are collinear |
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