Question

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

Answer #1

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 vector and parametric equations for:
a) the line that passes through the point P(9,-9,6) parallel to
the vector u = <3,4,-2>
b) the line passing through the point P(6,-2,6) parallel to the
line x=2t, y = 2 - 3t, z = 3 +6t
c) the line passing through the point P(5, -2,1) parallel to the
line x = 3 - t, y = -2 +4t, z = 4 + 8t

1)Find sets of parametric equations and symmetric equations of
the line that passes through the two points. (For the line, write
the direction numbers as integers.)
(5, 0, 2), (7, 10, 6)
Find sets of parametric equations.
2) Find a set of parametric equations of the line with the given
characteristics. (Enter your answer as a comma-separated list of
equations in terms of x, y, z, and
t.)
The line passes through the point (2, 1, 4) and is parallel to...

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 vector equation and parametric equations for the
line.
-The line that passes through the point
(2,2.4,3.5)
-The line that passes through point 81.0.6) and is
perpendicular to the plane x + 3y + z = 5

Find the parametric and symmetric equations of the line that is
parallel to the line x = 2 - 3t, y = 4 + t, z = -5 + 4t and passes
through the point (1, -4, 7)

(a) Find parametric equations for the line through
(5, 3, 6)
that is perpendicular to the plane
x − y + 3z = 1.
(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 sets of parametric equations and symmetric equations of the
line that passes through the given point and is parallel to the
given vector or line. (For each line, write the direction numbers
as integers.) Point Parallel to (−6, 0, 2) v = 3i + 4j − 7k
(a) parametric equations (Enter your answers as a
comma-separated list.)
(b) symmetric equations 3x = y 4 = 7z x 3 = y = z 7 x + 6 3 = y...

(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) =

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)

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