Question

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.)

°

Answer #1

Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z =
5
(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.) °

1) Find an equation of the plane. The plane through the point
(7, 0, 4)and perpendicular to the line x = 3t,y = 3 − t,z = 1 +
7t
2) Consider the following planes.x + y + z = 2, x + 6y + 6z =
2
(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...

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

Complete the parametric equations for the line where the planes
−10x + 7y + 3z = −27 and -7x + 3y - z= -7 intersect. x(t) =
−16t

Find the angle between the planes 15x−25y+z=−18 and
9x+3y+19z=−6. Round to the nearest degree, and do not include the
degree symbol in your answer.
Find the parametric equations for the line segment between the
points P(−3,5,9) and Q=(4,−7,2) so that the line segment extends
from P at t=0 to Q at t=1. Enter the three coordinate equations in
the form x=f(t), y=g(t), z=h(t).
Find an equation of the sphere that has center C(2,4,5) and is
tangent to the xy-plane.
Find...

Consider the system of linear equations 2x+y-3z=-7 x+y-z=-1
4x+3y-5z=-9 (a)Represent this system as a matrix A (b)Use row
operations to transform A into row echelon form Use your answer to
(b) to find all non-integer solutions of the system

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.

Find parametric equations for the line through (1, 1, 6) that is
perpendicular to the plane x − y + 3z = 8. (Use the parameter t.)
(x(t), y(t), z(t)) = 1+t, 1-t, 6+3t Correct: Your answer is
correct.
(b) In what points does this line intersect the coordinate
planes? xy-plane (x, y, z) = yz-plane (x, y, z) = xz-plane (x, y,
z) =

For a real number "a", consider the system of equations:
x+y+z=2
2x+3y+3z=4
2x+3y+(a^2-1)z=a+2
Which of the following statements is true?
A. If a= 3 then the system is inconsistent.
B. If a= 1 then the system has infinitely many solutions.
C. If a=−1 then the system has at least two distinct
solutions.
D. If a= 2 then the system has a unique solution.
E. If a=−2 then the system is inconsistent.

Complete the parametric equations for the line where the planes
− 2 y − 12 z = − 8 and − 6 x + 7 y − 3 z = − 17 intersect. x ( t )
= 90 t. Find y ( t ) and z ( t ).

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