Question

Find the point(s) of intersection, if any, of the line x-2/1 = y+1/-2 = z+3/-5 and the plane 3x + 19y - 7a - 8 =0

Answer #1

Find the point of intersection of the line
x(t) = (0, 1, 3) + (–2, – 1, 2)t
with the plane 4x + 5y – 4z = 9. And
Find the distance from the point (2, 3, 1) to the plane 3x
– 2y + z = 9

Find a plane containing the point (2,8,6) and the line of
intersection of the planes − 8 x + 5 y + 7 z = 126 and 8 x + 4 y +
4 z = − 24.

Show that the two lines with equations (x, y, z) = (-1, 3,
-4) + t(1, -1, 2) and (x, y, z) = (5, -3, 2) + s(-2, 2,
2) are perpendicular. Determine how the two lines
interact.
Find the point of intersection of the line (x, y, z) = (1,
-2, 1) + t(4, -3, -2) and the plane x – 2y + 3z =
-8.

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
(−1, 1, 3)
and contains the line of intersection of the planes
x + y − z = 4 and 3x − y + 4z = 3

Find the point of intersection of the lines (x-2) / - 3 = (y-2) / 6
= z-3 y (x-3) / 2 = y + 5 = (z + 2) / 4. Write the answer as (a, b,
c). If they are not cut, write: NO

1. Determine whether the lines are parallel, perpendicular or
neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 =
(z-2)/6
2. A) Find the line intersection of vector planes given by the
equations -2x+3y-z+4=0 and 3x-2y+z=-2
B) Given U = <2, -3, 4> and V= <-1, 3, -2> Find a. U
. V b. U x V

1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) =
(2y − z, x − z, y + 3x). Use matrices to find the composition S ◦
T.
2. Find an equation of the tangent plane to the graph of x 2 − y
2 − 3z 2 = 5 at (6, 2, 3).
3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...

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 4x − y + 5z = 5

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