Question

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.

Answer #1

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

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

3×3 Systems Elimination by Addition
1) 4x-2y-2z=2
-x+3y+2z=-8
4x-5y+z=11
2)-5x-2y+20z=-28
2x-5y+15z=-27
-2x-2y-5z=-12
Please show every step in clear handwriting, so I can
figure out how to do it myself.

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

Find the angle, in degrees, between the planes 2x-3y+6z=5 and
x-2y+2z=4. Respond the obtuse angle between both planes,
approximating to the nearest integer.

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

Find the angle, in degrees, between the planes 2x-3y + 6z = 5 and x-2y + 2z = 4. Answer the obtuse angle between the two planes, approximated to the nearest integer.

Consider the following planes.
x + y + z = 1, x + 3y + 3z = 1
(a) Find parametric equations for the line of intersection of
the planes. (Use the parameter t.)
(x(t), y(t), z(t)) =
(b) Find the angle between the planes. (Round your answer to one
decimal place.)
°

Determine the equation of the line of intersection of the two
planes 5x-2y-2z=1 and 4x+z=6.

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

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