Question

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

Answer #1

. Find the intersection of the planes x − y + 5z = 9 and
x = 1 + s − t
y = 1 +2 s − t
z = 2 − s + t .
(a) Find the line ℓ1 perpendicular to the first of these planes
and passing across the point (1, 2, 2).
(b) Find a line ℓ2 perpendicular to the second of these planes
and passing across the point (1, 2, 2).
(c) Find the...

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...

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.)
°

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...

find the parametric equation of the line passing through the
point (1,7,2), parallel to the plane x+y+z=2 and perpendicular to
the line x=2t, y=(3t+5)2, and z=(4t-1)/3

Find an equation of the plane.
The plane through the point
(1, 0, 3)
and perpendicular to the line
x = 6t, y = 6 − t, z = 5 + 3t

(a) Find parametric equations for the line through
(2, 2, 6)
that is perpendicular to the plane
x − y + 3z = 7.
(Use the parameter t.)
(x(t), y(t), z(t)) =
(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) =

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) =

Find the equation for the line through the point (2,0,2),
parallel to the plane x+y+z=10 and orthogonal to the line
r(t)=<1+t,1-t,2t>

1/ Find linear equation for the plane containing (-1,2,1) that
is parallel to the plane 2x - y + 3z = 1
2/ Find linear equation for the plane containing (2,0,9) that is
perpendicular to the line (x-2)/5 = (y+4)/3 = z/2

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