Question

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
the line given by * x* =

3) ind the distance between the planes 5x − 3y + z = 6 and 5x − 3y + z = −7.

Answer #1

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...

Find the VECTOR, PARAMETRIC and if possible SYMMETRIC equations
for the line through the point ( 5 , 6, 10 ) and parallel to the
line: [ x, y, z ] = [6 , 1 ,1 ] + t [4, 1, 5 ]

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 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 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

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)

Find a vector equation, parametric equations, and symmetric
equations for the line through the point (6, -5, 2) and parallel to
the vector < 1, 3, − 2 3 >

(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 the symmetric equations for the line that passes through
the point and is parallel to the vector . Also determine
the point of intersection that the line makes with
the plane.

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) =

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