Find equation of plane through the point (3,4,-1) which is parallel to

1.	Find equation of plane through the point (3,4,-1) which is parallel to plane vector r.(2i - 3j + 5k) + 7 = 0.
Answer» Let equation of any plane parallel to the given plane is given by vector r(2i - 3j + 5k) = d ...(i) If this plane passes through the point (3,4,-1) whose position vector is 3i + 4j - k Then, (3i + 4j - k).(2i - 3j + 5k) = d 3.2 + 4.(-3) + (-1).5 = d d = -11 By (i) we get vector r.(2i - 3j + 5k) + 11 = 0 which is the required equation of the plane.

Find equation of plane through the point (3,4,-1) which is parallel to plane vector r.(2i - 3j + 5k) + 7 = 0.

Answer»

Let equation of any plane parallel to the given plane is given by

vector r(2i - 3j + 5k) = d ...(i)

If this plane passes through the point (3,4,-1) whose position vector is 3i + 4j - k

Then, (3i + 4j - k).(2i - 3j + 5k) = d

3.2 + 4.(-3) + (-1).5 = d

d = -11

By (i) we get vector r.(2i - 3j + 5k) + 11 = 0

which is the required equation of the plane.