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Three Dimensional Geometry

Question

Show that the points (–1, 2, –3), (4, 5, 1) and (9, 8, 5) are collinear.

Solution

Let P(– 1, 2, – 3), Q(4, 5, 1) , R(9, 8, 5) be given points.
The direction ratios of PQ are 4 + 1, 5 – 2, 1 + 3 i.e. 5, 3, 4,
The direction ratios of PR are 9 + 1, 8 – 2, 5 + 3, i.e. 10, 6, 8.
Since $10 over 5 space equals 6 over 3 space equals space 8 over 4$
∴ lines PQ and PR are parallel.
But P is a common point on both lines.
∴ points P, Q, R are collinear.

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Three Dimensional Geometry

Show that the points (–1, 2, –3), (4, 5, 1) and (9, 8, 5) are collinear.

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Show that the points (–1, 2, –3), (4, 5, 1) and (9, 8, 5) are collinear.

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.