Question

1. A plane passes through *A(1, 2, 3), B(1, -1, 0)* and
*C(2, -3, -4)*. Determine vector and parametric equations of
the plane. You must show and explain all steps for full marks. Use
AB and AC as your direction vectors and point A as your starting
(x,y,z) value.

2. Determine if the point (4,-2,0) lies in the plane with vector
equation *(x, y, z) = (2, 0, -1) + s(4, -2, 1) + t(-3, -1,
2)*.

Answer #1

A (–4, –1, 2), B (3, –2, –1) and C (–1, 3, –4),
AB= 7? − ? − 3?
CB = 4? − 5? + 3?
AC = 3? + 5? - 2?
Question 7: Express the vector AC as the sum of two vectors: AC
= ? + ?, where ? is parallel to the vector CB and ? is
perpendicular to CB. Given that AC ∙ CB = −26 and that CB = √50,
determine the y-component of...

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 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...

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...

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 equation of the plane that contains the line
(x-2)(1/3)=(y)(1/2)=(z+4) and passes through the point P(1, 0,
-2)

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 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

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 4x − y + 5z = 5

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