Question

Find the angle between the planes 15x−25y+z=−18 and 9x+3y+19z=−6. Round to the nearest degree, and do not include the degree symbol in your answer.

Find the parametric equations for the line segment between the points P(−3,5,9) and Q=(4,−7,2) so that the line segment extends from P at t=0 to Q at t=1. Enter the three coordinate equations in the form x=f(t), y=g(t), z=h(t).

Find an equation of the sphere that has center C(2,4,5) and is tangent to the xy-plane.

Find the distance between the points (2,−4,7) and (−3,−2,1). Give an exact answer.

Answer #1

Consider the following planes.
x + y + z = 1, x + 3y + 3z = 1
(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 place.)
°

(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 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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