Line & Planes In Space

Line In Space

100

Determine whether point lies on the line.x = −4 + t, y = 4t, z = 7 + t

    (0, 16, 11)

Bloolean User = True;

200

Find sets of parametric equations and symmetric equations of the line through the point parallel to the given vector or line (if possible). Point Parallel to(-1, 7, 2) 

x − 1/3 = y + 1/−4 = z − 5

X=3t-1, y=-4+7, z=t+2

300

Find an equation of the plane.The plane passes through (0, 0, 0), (4, 0, 6), and (−2, −1, 8).

6x-44y-4z=0

400

Find an equation of the plane.The plane passes through the points (4, 3, 1) and (4, 1, -7) and is perpendicular to the plane 6x + 8y + 2z = 12.

60x − 48y + 12z = 108

Distance: Point,Line,Plane

100

What is midpoint of the 2 points and the distance between P1 and midpoint.

P1: (4,5,12)

P2: (9,23,9)

( 13/2, 14, 21/2 )

Distance: 9.46

200

Find the distance between the point and the plane. (Round your answer to three decimal places.)

(1, 6, 5)
x − y + 2z = 6

0.408

300

Find the distance between the point and the line given by the set of parametric equations. (Round your answer to three decimal places.)

(3, -3, 1); x = 2t, y = t − 3, z = 2t + 2

2.867

400

Who is the coolest teacher at Valley! 

MRS. SHAK!!!!!!!!

Relationship

100

Determine if any of the lines are parallel or identical. (Select all that apply.)

L1: x = 8 − 4t,    y = −3 + 3t,    z = 5 + 6t

L2: x = 8t,    y = 3 − 6t,    z = 17 − 12t

L3: x = 10 − 8t,    y = 4 + 6t,    z = 8 + 12t

L4: x = −6 + 8t,    y = 4 + 6t,    z = 5 − 8t

1,2,3

200

Determine whether the plane passes through each point.x + 6y − 3z − 1 = 0 

(a)    (−14, 2, −1)

(b).   (7, 2, 3)

YES
NO

300

4x − y + z = 6

Find x, y, z Intercepts.

x-intercept: (x, y, z)  = (3/2,0,0)
y-intercept: (x, y, z)  = (0,-6,0 )

z-intercept: (x, y, z)  = (0,0,6)

400

Determine whether the planes are parallel, orthogonal, or neither.

3x − 15y − 3z = 9

3x − 15y − 3z = −2

Now find the angle!!!!!

Parallel 

Angle Does not exist