A plane has normal vector n and passes through the point P n

A plane has normal vector n and passes through the point P. n = 7i - j + 2k, P(0, 2, -2) Find an equation for the plane. ________________ Find the intercepts. (If an answer does not exist, enter DNE.) x-intercept x=_______________ y- intercept y = _______________ z-intercept z = ___________

Solution

equation of plane is ax+by+cz=d

n= 7i - j + 2k

Therefore a=7,b=-1 and c=2

And it passes through (0,2,-2)

So we get 7(0)-1(2)+2(-2)=d

d=-6

Therefore the equation of the plane is

7x -y+2z=-6

to find x intercept,we have to plug y=0 and z=0

so we get

7x=-6

x=-7/6

and that\'s the xintercept

and to find y intercept,we have to plug x=0 and z=0

-y=-6

y=6 and that\'s the y intercept

And for z intercept ,we have to plug x and y both to zero

and we get

2z=-6

z=-3