Question

(1 point) Find the simplest vector parametric expression r⃗ (t) for the line that passes through the points P=(5,3,−2) at time t = 4 and Q=(8,−1,−3) at time t = 10

Answer #1

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

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

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 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 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

Find a vector equation and parametric equations for the line.
(Use the parameter t.)
The line through the point
(0, 12, −8)
and parallel to the line
x = −1 + 3t,
y = 6 − 4t, z
= 3 + 6t

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 >

Find (a) a vector-valued function, (b) parametric equations, and
(c) a Cartesian equation for the line that is parallel to the
vector <−2, 6> and passes through the point P(−4, 5)

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...

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