Question

1. Solve all three:

a. Determine whether the plane 2x + y + 3z – 6 = 0 passes through the points (3,6,-2) and (-1,5,-1)

b. Find the equation of the plane that passes through the points (2,2,1) and (-1,1,-1) and is perpendicular to the plane 2x - 3y + z = 3.

c. Determine whether the planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection:

3x + y - 4z = 3 and -9x - 3y + 12z = 4

Answer #1

Determine whether the planes x−2y+3z−4 = 0 and −2x+5y+4z = −1
are orthogonal.

given the planes P1 and P2 determine whether the planes intersect
or are parallel. if they intersect, give the direction vector for
thr line of intersection. P1:3x+y-3z=4
p2:2x+3y+2z=6

Let P be the plane given by the equation 2x + y − 3z = 2. The
point Q(1, 2, 3) is not on the plane P, the point R is on the plane
P, and the line L1 through Q and R is orthogonal to the plane P.
Let W be another point (1, 1, 3). Find parametric equations of the
line L2 that passes through points W and R.

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

1. Determine whether the lines are parallel, perpendicular or
neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 =
(z-2)/6
2. A) Find the line intersection of vector planes given by the
equations -2x+3y-z+4=0 and 3x-2y+z=-2
B) Given U = <2, -3, 4> and V= <-1, 3, -2> Find a. U
. V b. U x V

Find an equation of the plane.
The plane that passes through the line of intersection of the
planes
x − z = 2 and y + 3z = 1
and is perpendicular to the plane
x + y − 3z = 3

Find an equation of the plane. The plane that passes through the
point (−3, 3, 2) and contains the line of intersection of the
planes x + y − z = 2 and 2x − y + 4z = 1

Find the line intersection and the angle between the planes
3x-2y+z=1 and 2x+y-3z=3.

Find an equation for each of the following planes. Use x, y and
z as the variables.
a) An equation of the plane passing through the points (1,−1,1),
(0,−2,−1) and (−4,0,6)
b) An equation of the plane consisting of all points that are
equidistant (equally far) from (−3,−5,−1) and (4,−1,−3)
c) An equation of the plane containing the line
x(t)= [0, -1, 1] + t[0, 4, -1] and is
perpendicular to the plane 3y − 4z = −7

a. Determine an equation of the line of intersection of the
planes 4x − 3y − z = 1 and 2x + 4y + z = 5.
b. Find the scalar equation for the plane through (5, −2, 3) and
perpendicular to that line of intersection.

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