The x -intercept of the plane which is passing through the intersection of the planes x + 2 y + 3 z + 5 = 0 and 2 x − 3 y + 7 z + 1 = 0 and parallel to line r = i ^ + 2 j ^ + λ ( 8 i ^ − 7 j ^ − 4

Question

The x -intercept of the plane which is passing through the intersection of the planes x + 2 y + 3 z + 5 = 0 and 2 x − 3 y + 7 z + 1 = 0 and parallel to line r = i ^ + 2 j ^ ​ + λ ( 8 i ^ − 7 j ^ ​ − 4 k ^ ) , is-

TestHub · Accepted Answer

Required plane ( 1 + 2 λ ) x + ( 2 − 3 λ ) y + ( 3 + 7 λ ) z + 5 + λ = 0 it is parallel to given line ⇒ ( 1 + 2 λ ) i ^ + ( 2 − 3 λ ) j ^ ​ + ( 3 + 7 λ ) k ^ . ( 8 i ^ − 7 j ^ ​ − 4 k ^ ) = 0 ⇒ 8 ( 1 + 2 λ ) − 7 ( 2 − 3 λ ) − 4 ( 3 + 7 λ ) = 0 ⇒ λ = 2 x intercept = 1 + 2 λ − 5 − λ ​ = − 5 7 ​

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