#3D coordinates

Vectors and 3D Geometry

Find the angle between the line x + 12 = y;3 = z - 36 and the plane 10x + 2y - 11z - 3 = 0.

Understanding this is easy: we verify ^ - 1( 8/21 ) by full calculation: use standard identity, substitute, simplify step by step to reach ^ - 1( 8/21 ).

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

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Vectors and 3D Geometry

XY-plane divides the line joining the points A(2, 3, -5) and B(-1, -2, -3) in the ratio

Here's the idea in simple terms: we verify 5 ∶ 3 externally by full calculation: use standard identity, substitute, simplify step by step to reach 5 ∶ 3 externally.

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

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General Mathematics 1

The value of k such that the line x-4/1=y-2/1=z-k/2 is lying on the plane 2x - 4y + z = 7 will be?

Think of it like this: solving fully: apply relevant formula, put numbers, compute. Result comes as 7. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI and XII

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Vectors and 3D Geometry

If the direction cosines of a line are (1/k, 2/k, -2/k) then k is

Let's break it down: after simplifying, ± 3 is left. The method is simple: formula → substitution → calculation → answer.

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

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