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Find the ratio in which the (i) xy – plane (ii) yz – plane (iii) zx – plane divides the line segment formed by joining the points (x1, y1, z1) and (x2, y2, z2). |
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Answer» We have, the coordinates of a point dividing the line joining the points A (x1, y1, z1) and B (x2, y2, z2) in the ratio k : 1 are, P = ((kx2 + x1)/(k + 1), (ky2 + y1)/(k + 1), (kz2 + z1)/(k + 1)) (i) If xy – plane divides a line segment joining the given points, A, B, then z – coordinate of P is zero. i.e., (kz2 + z1)/(k + 1) = 0 ⇒ kz2 + z1 = 0 ⇒ k = - z1/z2 ∴ xy-plane divides the line segment AB in the ratio -z1 : z2 Similarly, (ii) The yz-plane in the ratio -x1: x2 (iii) The zx-plane in the ratio -y1 : y2 |
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