orthogonal planes calculus?
A plane P is orthogonal to the line L: x=3-2t, y=1+5t, z=4-t, and passes through the point (8,9,6).
a.Find equation of the plane P. (standard form)
b. Find the point where the plane P intersects the z-axis.
More Questions From This User See All
Answers & Comments
Verified answer
a) The direction vector of the line, which is <-2, 5, -1>, is normal to the plane.
So, the plane has equation <-2, 5, -1> · <x - 8, y - 9, z - 6> = 0
==> -2(x - 8) + 5(y - 9) - (z - 6) = 0.
b) When the plane intersects the z-axis, both x = 0 and y = 0.
So, -2(0 - 8) + 5(0 - 9) - (z - 6) = 0
==> z = -23.
I hope this helps!