The line of intersection of the planes r (3 i - j + k ) = 1 and r ( i + 4 j - 2 k ) = 2, is:

JEE Main 2017 Mathematics question

The line of intersection of the planes and , is:

Answer: (3)

The line of intersection is perpendicular to both normals, so its direction is their cross product:

(3,-1,1)×(1,4,-2) = i(2-4) - j(-6-1) + k(12+1) = (-2,\ 7,\ 13).

Next find one point on the line. Setting reduces the two plane equations to

3x - y = 1, x + 4y = 2.

From the first,

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Question ID VK-115851