Question

Find the projection of the point (7,0,5) on the plane 3x-y+2z=3

Thanks!

Answer #1

a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0 = (5, 2, 1) to T, and the point Q in T that is
closest to P0. Use the square root symbol where needed.
d=
Q= ( , , )
b) Find all values of X so that the triangle with vertices A =
(X, 4, 2), B = (3, 2, 0) and C = (2, 0 , -2) has area (5/2).

shows that the 3x-6y + 2z = 5 plane is parallel to the line x = 1 +
9t, y = 5-4t, z = 9-t and calculates the distance between the
two

Consider the linear transformation P : R3 → R3 given by
orthogonal projection onto the plane 3x − y − 2z = 0, using the dot
product on R3 as inner product.
Describe the eigenspaces and
eigenvalues of P, giving specific
reasons for your answers. (Hint: you do not need
to find a matrix representing the transformation.)

Find an equation of the plane.
The plane that passes through the point
(−1, 1, 3)
and contains the line of intersection of the planes
x + y − z = 4 and 3x − y + 4z = 3

Find an equation of the plane perpendicular to x+y−2z = 1 and that
contains the intersection of x − z = 10 and y + 2z =
11.

Find the equation of the tangent plane of the surface implicitly
defined by xy^2z^3=8 at the point (2,2,1).

Find the maximum and minimum values of the function
f(x,y,z)=3x−y−3 subject to the constraints x^2+2z^2=324 and
x+y−z=−6 . Maximum value is , occuring at ( , , ). Minimum value is
, occuring at ( , , ).

Consider plane P: 4x -y + 2z = 8, line: <x, y, z> =
<1+t, -1+2t, 3t>, and point Q(2,-1,3)
b) Find the perpendicular distance between point Q and plane
P

Find the point on the line 3x + y = 7 that is closest to the
point (−4, 3)
(x,y) =

show that
L: x=-1+t , y=3+2t ,z=-t
and the plane P : 2x-xy-2z=-3
are parallel then find the distance btween them

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