Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t Find two distinct points Q1 and Q2 on the line L at distance 3 to the plane P.

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

A:

Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

A:

Q: Find an equation of a plane containing the line r = (4, –5, –4) + t (–7, 8, –4) which is parallel to…

A:

Q: Consider the plane P with equation -2x+y-2z -6 and line L with equations x=-1-2t y 5+2t z =-7-6t…

A: Distance of (a,b,c) from the plane mx+ny+oz=p is given by (ma+nb+oc-b)/sqrt(m^2+n^2+o^2)

Q: Find the line r that passes through the origin and is perpendicular to the π planes that passes…

A:

Q: Show that the planes given by y − 7z = 16 and 2y − 14z = 5 are parallel, and find the distance…

A:

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

Q: Find the intersection of the plane 4x – 6y – 7z = 10 and the line r(t) = (- 8, – 3, 3)t + (4, 1, 5).…

A:

Q: Consider the plane P with equation x-2y+2z = 3 and line L with equations x = 8+6t y =-1-2t z = 1+4t…

A: Line and plane

Q: Consider the plane P with equation -2x-2y+z = -1 and line L with equations x = 1-4t y =-1-2t z =…

A:

Q: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

A:

Q: Consider the plane P with equation -2x+2y-z =3 and line L with equations x= -3-3t y = 3+7t z= 21…

A:

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: Consider the plane P with equation 2x+y-2z = 4 and line L with equations x =-5+2t Ly =-5+6t z = 4-4t…

A: Given equation of plane P is 2x+y−2z=4 and equations of line are x=−5+2t, y=−5+6t, z=4−4t. And given…

Q: Determine if the plane given by -x + 2z 10 and the line given by %3D (x = 5, y = 2 -t,z = 10 + 4t)…

A: given plane: -x+2z+10 given line: (5,2-t,10+4t)

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

A:

Q: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: 3. Find the distance from P(1, 1, 1) to the plane II with equation r – 3y + 4z = 10.

A: Distance between point and plane is (4√26)/13.

Q: Consider the plane P with equation -2x-2y+z=-3 and line L with equations x= 7-4t y = 7-6t z =-2-2t…

A: Use distance formula to find Q1,Q2

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

A:

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x = −6+t,…

A:

Q: Consider the plane P with equation 2x-2y+z =4 and line L with equations x= 3+2t y =-1-5t z= 5+4t…

A: Solved below

Q: Consider the plane P with equation -x+2y-2z = -3 and line L with equations x = 2 y = 9+5t z =-4-4t…

A:

Q: Find the equation of the plane containing the point P(-2,4,3) and the line y+1 z+2 %3D 4 2 -3

A:

Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: Find an equation of the plane containing the points P(O,0,o) and Q(2,2,2) and parallel the line…

A: Given:- Equation of line x= t, y = 1,z= t  To find:- An equation of the plane containing the points…

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: Q1. A) Determine if the plane given by -x + 2z = 10 and the line given by %3D (x = 5,y = 2 - t,z =…

A: Consider the given values. -x+2z=10 And, (x=5, y=2-t, z=10+4t)

Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

A:

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

A:

Q: Consider the plane P with equation x+2y+2z =-10 and line L with equations x =-1+2t y =-1+3t z = 1+5t…

A:

Q: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Show that the planes are orthogonal.

A: Given: 3x+6z=12x+2y−z=3

Q: Consider the plane P with equation −2x−2y−z = −11 and line L with equations x = 1−3t y = −1−6t z = 2…

A:

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: Find the plane determined by the intersecting lines. L1 x= - 1+ 3t y =2 +3t z =1- 4t L2 x= 1-4s y =…

A: Given :-  The plane determined by the intersecting lines. L1    :   x = -1 + 3t    ,    y = 2 + 3t…

Q: Consider the plane P with equation −2x+2y−z = −5 and line L with equations x = 9−4t y = −5+2t z =…

A: Consider the plane P with equation −2x+2y−z = −5 and Line with equations x = 9−4t y = −5+2t z = 4−6t

Q: Find an equation of the plane through (-8, 4, –9) that is perpendicular to the planes 5x – y +z = 1…

A: Solution of question is written in below steps.

Q: Consider the plane P with equation −2x−2y+z = 1 and line L with equations x = 2−3t y = 9−6t z = −4…

A:

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

A:

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

A:

Q: Are the plane 2x-y-4z 10 and the line {x = 2+4t,y 5- 2t,z =-8t} parallel or orthogonal?

A: We have to find out

Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

A: