Equations of Lines and Planes

Find the distance from the point (-6, 3, 5) to the plane x - 2y - 4z = 8. Round to thousandths.

• 8.729

• 6.983

• 3.320

• 3.712

Which of the following represents the parametric equations of a line in three-dimensional space?

Find the point at which the line given by the parametric equations below intersects the plane.

2x + 4y - 3z = -48

x = 10 + 7t

y = -10

z = 7t

• (-38, -10, 28)

• (43, -10, -18)

• (38, -10, 28)

• (-43, -10, 18)

• (38, -10, -28)

Find parametric equations for the line through the point (4, 5, 2) that is parallel to the plane x + y + z = -15 and perpendicular to the line x = 15 + t, y = 12 - t, z = 3t.

• x = 4t + 4, y = -2t + 5, z = -2t + 2

• x = 2t + 4, y = -4t + 5, z = 2t + 2

• x = 4t - 4, y = -2t - 5, z = -2t + 2

• x = 4t, y = 2t - 5, z = -2t

• x = 4t - 4, y = -2t, z = -2t + 5

Find the distance between the planes. 5x - 2y + z - 1 = 0, 5x - 2y + z + 4 = 0

• 1/6

• √30/6

• 5/6

• √30

• 5√30/6

Identify the planes that are perpendicular.

• x + 10y - z = 6, -9x - y - 19z = 2

• x = 5x + 3y, -10x - 6y + 2z = -1

• 8x + 5y = -3, 9y + 6z = -1

• 8x + 5y = -3, y + 6z = -1

• 7x + 4y = -3, 9y + 6z = 1

Find the distance between the given parallel planes. 6x + 7y - 2z = 10 and 12x + 14y - 4z = 60

• 3.42

• 2.13

• 2.12

• 3.14

• 5.12

Find an equation of the plane through the points (0, 3, 3), (3, 0, 3) and (3, 3, 0).

• x + y + z = 6

• 9x - 6y - 9z = 1

• x + y + z = 3

• x + 3y + z = 1

• x - y + z = 1

Find an equation of the plane with x-intercept = 7, y-intercept = 6 and z-intercept = 3.

Which of the following lines is PARALLEL to the graph of 5x + 2y = 8?

• 2x + 5y = 8

• 5x - 2y = 6

• -10x - 4y = 7

• -10x + 4y = 9