Question

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

Answer #1

4. Consider the planes x + 2y − 2z = −4 and 2x − 5y − z + 11 =
0. i. Determine parametric equations for the line of intersection
of the planes. ii. Determine the dihedral angle between the planes
as an exact value.

Solve each system by elimination.
1) -x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20
2) -4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4
3) -x-5y+z=17
-5x-5y+5z=5
2x+5y-3z=-10
4) 4x+4y+z=24
2x-4y+z=0
5x-4y-5z=12
5) 4r-4s+4t=-4
4r+s-2t=5
-3r-3s-4t=-16
6) x-6y+4z=-12
x+y-4z=12
2x+2y+5z=-15

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...

Find the parametric equations of the line in which the planes
x+2y+4z=1and -2x-2y+z=4 intersect.

Solve the linear system by Gaussian elimination. 2x+2y+2z= 0
–2x+5y+2z= 1 8x+ y+4z=–1

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

Given the parallel planes x + 2y + 3z = 1 and 3x + 6y + 9z = 18.
Find a normal vector to these planes.

Find a nonzero vector parallel to the line of intersection of
the two planes 2z−(2x+5y)=4 and y+3z=2

for 10-12 you will solve the following system of equations:
2x+y+z=-2 2x-y+3z=6 3x-5y+4z=7 10) what is the solution for x? a)2
b)-3 c)infinitely many solutions d)no solution 11) what is the
solution for y? a)2 b)0 c)inifinitely many solution d)no solution
12) what is the solution for z? a)4 b)-8 c)infinitely many
solutions d)no solutions

Solve the system of equations. Explain how please!
3x-5y+4z= -19
4x-3y-3z= -34
x-y+4z = 13

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