Question

Find a parametrization for the line perpendicular to (2, −1, 1), parallel to the plane 2x + y − 6z = 1, and passing through the point (1, 0, −3). (Use the parameter t. Enter your answers as a comma-separated list of equations.)

Answer #1

Find a parametrization for the line perpendicular to
(4, −1, 1),
parallel to the plane
4x + y −
8z = 1,
and passing through the point
(1, 0, −7).
(Use the parameter t. Enter your answers as a
comma-separated list of equations.)

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 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 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 a set of parametric equations of the line with the given
characteristics. (Enter your answers as a comma-separated
list.)
The line passes through the point
(−2, 8, 6)
and is perpendicular to the plane given by
−x + 2y +
z = 8.

Find parametric equations of the line that passes through (1, 2,
3) and is parallel to the plane
2 x − y + z = 3 and is perpendicular to the line with parametric
equations:
x=5-t, y=3+2t , z=4-t

Find parametric equations of the line that passes through (1, 2,
3) and is parallel to the plane
2 x − y + z = 3 and is perpendicular to the line with parametric
equations:
x=5-t, y=3+2t, z=4-t

Determine the symmetric and parametric equations of the
line:
(A.) parallel to the z-axis passing through the point (1, 2, 1)
(b.) Parallel to the line (1-2x)/3 = y/4 = (2z + 1)/4 and
passing through the point (2, 1, 0)
(c.) Perpendicular to the straight R defined by r: X = (2,-1, 2)
+ t (1, 2,-1) and passes through Point P (3, 2, 1)

(a) Find the unit vectors that are parallel to the tangent line
to the curve
y = 2 sin x
at the point (π/6, 1). (Enter your answer as a
comma-separated list of vectors.)
(b) Find the unit vectors that are perpendicular to the tangent
line.

Find parametric equations of the line through the point (2, 1,
0), perpendicular to the plane containing (1, −1, 1), (3, −1, 2)
and (0, 0, 1)

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