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Q.

which of the following lines lie on the plane x+ 2y - z + 4= 0?

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a

x-y+z=2x+y-z=0

b

 r=2i^j^+4k^+λ(3i^+j^+5k^)

c

x11=y1=z51

d

none of these

answer is A, C.

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Detailed Solution

For line x11=y1=z51 point (1, 0, 5) lies on 1-1-ln^n the plane .

Also, the vector along the line i^+j^+k^ is perpendicular to the normal i^+2j^-k  to the plane.  For line r=2i^j^+4k^+λ(3i^+j^+5k^)

 point (2, -1,4) lies on the plane and vector 3i^+j^+5k^ is perpendicular to the normal i^+2j^k^

Line x - y + z = 2x + y - z= 0 passes through the origin, which is not on the given plane.

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