Which of the following planes intersects the planes x-y+2z=3 and 4x+3y-z=1 along the same line?

JEE Advanced Mathematics question

Which of the following planes intersects the planes and along the same line?

(A)Correct
(B)
(C)
(D)none of these

Answer: (A)

Solution

The required plane must contain the common line, so it has the form . - (a) has no constant term, so and . This gives , i.e. ✓. - (b) also passes through the origin, so it would need too, but that gives

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Question ID VK-109887