Question

verify whether the line x-3/-4=y-4/-7=z+3/12 lies in the plane 5x-y+z=8​

Answer 1

Answer:

for a given line to lie on a plane ,it must be perpendicular to the normal vector to the plane.

vector b = -4i-7j+12k     and normal vector n = 5i-j+k

if line lie on a plane the dot product of vector b and normal vector n must be zero

b.n = ( -4i-7j+12k).(5i-j+k)

    = -20+7+12

   -1 is not equal to 0

hence our line does not lie on a plane

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