Find the standard equation of the sphere with center (-3, 2, 4) that is tangent to the plane given by 2x + 4y - 3z = 8.

Find an equation of the plane. -The plane contains the y-axis and makes an angle of π/6 with the positive x-axis.

Verify that the lines are parallel, and find the distance between them. L_1: x = 2-t, y = 3+2t, z = 4+t L_2: x = 3t, y = 1 - 6t, z = 4 - 3t

Find the distance between the point and the line given by the set of parametric equations. (4, -1, 5); x = 3, y = 1 + 3t, z = 1 + t

Find the distance between the given parallel planes. 2x-3y+z=4, 4x-6y+2z=3

Find the distance between the point and the plane. (3, 1, -2); x + 2y -2z = 4

Determine whether the given planes are parallel. x - 4y - 3z - 2 = 0 and 3x - 12y - 9z - 7 = 0

Determine whether the given planes are perpendicular. x- 2y + 3z = 4, -2x + 5y + 4z = -1

Determine whether the following pairs of planes are parallel, orthogonal, or neither. x+y+4z=10 and -x-3y+z=10

Determine whether each statement is true or false. Two planes perpendicular to a third plane are parallel.

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection. L1: x = 3 + 2t, y = 4 - t, z = 1 + 3t L2: x = 1 + 4s, y = 3 - 2s, z = 4 + 5s

Find parametric equations for the line through the point (0,1,2) that is perpendicular to the line x=1+t, y=1-t, z=2t and intersects this line.

Find the coordinates of the point. What is the x-coordinate of any point in the yz-plane?

At rest, a light source emits 532 nm light, (a) As it moves along the line connecting it and Earth, observers on Earth see 412 nm. What is the source's velocity (magnitude and direction)? (b) Were it to move in the opposite direction at the same speed, what wavelength would be seen? (c) Were it to circle Earth at the same speed, what wavelength would be seen?