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Line of intersection of two planes - class-XII
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The line of intersection of the planes $\overrightarrow { r } .\left( 3\hat { i } -\hat { j } +\hat { k } \right) =1$ and $\overrightarrow { r } .\left( \hat { i } +4\hat { j } -2\hat { k } \right) =2$ is parallel to vector
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A
$-2\hat { i } +7\hat { j } +13\hat { k } $
💡 Explanation:
The line of intersection of two planes is parallel to the cross product of their normal vectors. The normals are n1 = (3, -1, 1) and n2 = (1, 4, -2). The cross product is (-1*-2 - 14, 11 - 3*-2, 34 - -11) = (2-4, 1+6, 12+1) = (-2, 7, 13).