Question

1a. Find a vector equation for the line segment from

(4, −3, 7) to (8, 3, 4). (Use the parameter
*t*.)

1b. Find an equation of the plane.

The plane through the point (7, 4, 9) and with normal vector
2**i** + **j** − **k
1c. **Find an equation of the plane.

The plane through the point

(2, −5, −9)

and parallel to the plane 6*x* − *y* − *z*
= 4

Answer #1

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 the equation of a line through the point (4, -3, 1) and is
perpendicular to the plane 2x – y + z = 6. Give the answer in
parametric form and in vector form.

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 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

Let a = 2i -3k; b= i+j-k
1) Find a x b.
2) Find the vector projection of a and b.
3) Find the equation of the plane passing through a with normal
b.
4) Find the equation of the line passing through the points a and
b.
Please help and show your steps. Thank you in
advance.

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 equation for the line through the point (2,0,2),
parallel to the plane x+y+z=10 and orthogonal to the line
r(t)=<1+t,1-t,2t>

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...

Evaluate the vector line integral F*dr of F(x,y) = <xy,y>
along the line segment K from the point (2,0) to the point (0,2) in
the xy-plane

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 ]

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