Three Dimensional Geometry

Question

Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) are collinear.

Solution

The given points are A(2, 3, – 4), B(1, –2, 3), C(3, 8, –11)
The direction ratios of the AB are 1 – 2, – 2 – 3, 3 + 4 i.e. – 1 – 5,1
The direction ratios of AC are 3 – 2, 8 – 3, –11 + 4 i.e. 1, 5, – 7
∴ direction ratios of AB and AC are proportional
∴ AB is parallel to AC.
But A is a common point on both the lines.
∴ A, B, C are collinear points.

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Three Dimensional Geometry

Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) 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.

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) 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.