#direction ratios

Vectors and 3D Geometry

What are the direction ratios of the line of intersection of the planes x = 3z + 4 and y = 2z - 3?

From the definition, using formula we get 〈3, 2, 1〉. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 〈3, 2, 1〉.

Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry

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Vectors and 3D Geometry

What are the d.c's of the line whose d.r's are 1. -2. and 3 ?

The logic is straightforward: we verify 1 14, 2 14, 3 14 by full calculation: use standard identity, substitute, simplify step by step to reach 1 14, 2 14, 3 14.

Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry

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Vectors and 3D Geometry

Find the direction ratios of the line 2x = 3y = 5 - 4z ?

We know that after simplifying, is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry

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Vectors and 3D Geometry

Find the value of k for which the line through the points (2, 4, 8) and (1, 2, 4) is parallel to the line through the po

We know that we verify 9 by full calculation: use standard identity, substitute, simplify step by step to reach 9.

Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry

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Coordinate Geometry

If the straight line x-x_0/l=y-y_0/m=z-z_0/n is parallel to the plane ax + by + cz + d = 0, then which one of the follow

Applying the basic concept, using formula we get al + bm + cn = 0. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get al + bm + cn = 0.

Ref: NCERT Mathematics Class XI — Coordinate Geometry

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