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JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

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Application +4 | -1
Assertion: The coordinates of the point which divides the join of A(2,−1,4){A}(2,-1,4) and B(4,3,2){B}(4,3,2) in the ratio 2:32: 3 externally is C(−2,−9,8)C(-2,-9,8)

Reason: If P(x1,y1,z1){P}\left({x}_1, {y}_1, {z}_1\right) and Q(x2,y2,z2){Q}\left({x}_2, {y}_2, {z}_2\right) be two points, and let R{R} be a point on PQ{PQ} produced dividing it externally in the ratio m1:m2{m}_1: {m}_2. Then the coordinates of R{R} are

(m1x2−m2x1m1−m2,m1y2−m2y1m1−m2,m1z2−m2z1m1−m2)\left(\frac{{m}_1 {x}_2-{m}_2 {x}_1}{{m}_1-{m}_2}, \frac{{m}_1 {y}_2-{m}_2 {y}_1}{{m}_1-{m}_2}, \frac{{m}_1 {z}_2-{m}_2 {z}_1}{{m}_{{1}}-{m}_2}\right)
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Correct option: A
Assertion is correct, reason is correct; reason is a correct explanation for assertion
Option A is correct because the assertion is true, the reason is true, and the reason correctly explains the assertion about external division of a line segment in 3D space.

More Questions from 3D GEOMETRY SYSTEM

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