Find a vectors perpendicular and parallel to the plane.

Question

(a) Find a vector n^-> perpendicular to the plane

z=7x+8y.

n^-> =

(b) Find a vector v^-> parallel to the plane.

v^->=

Answer 1

z=7x+8y.

the scalar inner product (7,8,-1)*(x-0,y-0,z-0)=0

means the two vectors are perpendicular (by setting the product =0, cos(π/2)=0)

and the product is the equation for plane,

normal vector is (7,8,-1)

vectors originate at origin so parallel vector wil be on plane

if x=1, z=8y+7, if y=1, z=15

so a vector parallel is (1,1,15)