InterviewSolution
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InterviewSolution
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In which ratio (3, 4, 5) divides the line segment joining (1, 2, 3) and (4, 5, 6) internally?(a) 1:2(b) 2:1(c) 3:4(d) 4:3I got this question in a job interview.My question is based upon Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 11 |
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Answer» RIGHT choice is (b) 2:1 For explanation: The coordinates of a POINT dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m: n is \((\FRAC{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n})\). Let the ratio be K : 1.So, the coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio k: 1 is \((\frac{k*4+1*1}{k+1},\frac{k*5+1*2}{k+1},\frac{k*6+1*3}{k+1})\) => \((\frac{k*4+1*1}{k+1},\frac{k*5+1*2}{k+1},\frac{k*6+1*3}{k+1})\) is same as (3, 4, 5). => (4k+1)/(k+1) = 3 => 4k+1 = 3k+3 => k = 2 So, ratio is 2:1. |
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