34 Consider the plane 3x 2y 7 z 3 0 a Give a normal vec

34. Consider the plane 3x + 2(y + 7) ? (z ? 3) = 0.

a) Give a normal vector for the plane.

b) Give a point on this plane.

c) Is the point (2, ?5, 9) on this plane?

Answers with explanation please!

Solution

Consider the plane 3x + 2(y + 7) ? (z ? 3) = 0.

a) Give a normal vector for the plane.

Normal vector will be nothing but the coefficient of the x,y,z in the plane

i.e vector=3i+2j-k

b) Give a point on this plane

(0.-7.3) is a point which satisfies the eqn and the given eqn can be seen as in a format which shows a plane passing through a particular point.

c) Is the point (2, ?5, 9) on this plane?

put into the eqn

the value coming to be =4 instead of 0,so not in the plane