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

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 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...

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.

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) 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 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 an equation of a sphere with the given radius r
and center C. (Use (x,
y, z) for the coordinates.)
r =
7; C(3, −5, 2)
Find the angle between u and
v, rounded to the nearest tenth degree.
u = j + k,
v = i +
2j − 5k
Find the angle between u and
v, rounded to the nearest tenth degree.
u = i + 4j −
8k, v =
3i − 4k
Find a vector that...

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 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...

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