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Q.

Consider a plane P passing through, A(λ,3,μ), B(1,3,2) and C(7, 5, 10) and a straight line L with positive direction cosines passing through A, bisecting BC and makes equal angles with the coordinate axes. Let L1 be a line, parallel to L and passing through origin. Then which of the following is/are true

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a

The value of (λ+μ) is 5

b

Equation of the straight line L1 is x11=y11=z11

c

Equation of the plane perpendicular to the plane P and containing the line L is x–2y+z=0

d

Area of the triangle ABC is 32 square units

answer is B, C, D.

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Detailed Solution

a) is obviously true as it can be observed from the standard equation of the plane and from the concept of family of planes for (b),(c),(d) use the formula of volume of tetrahedron

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