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Three Dimensional Geometry

Question

The projections of a directed line segment on the co-ordinate axes are 6, -3, 2. Find its length and direction cosines.

Solution

Let l, m, n be the direction cosines of the line and let the length of the line segment be r.
∵ projection of the line segment on the axes are 6, - 3, 2
∴ l r = 6, m r = – 3, n r = 2
Squaring and adding, we get,
(l² + m² + n²) r² = 36 + 9 + 4
∴ r² = 49 ⇒ r = 7
$therefore space space space straight l space equals space 6 over 7 comma space space straight m space equals negative 3 over 7 comma space straight n space equals 2 over 7$
$therefore$ length of line = 7 units.
and direction cosines of line are $6 over 7 comma space space minus 3 over 7 comma space 2 over 7.$

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Three Dimensional Geometry

The projections of a directed line segment on the co-ordinate axes are 6, -3, 2. Find its length and direction cosines.

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

The projections of a directed line segment on the co-ordinate axes are 6, -3, 2. Find its length and direction cosines.

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.