Consider the plane P with equation 2x-2y+z =4 and line L with equations x= 3+2t y =-1-5t z= 5+4t Find two distinct points Q, and Q, on the line L at distance 3 to the plane P. Q1 = (0,0.0) Q2 = (0,0.0)

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

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Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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

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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 =…

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

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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,…

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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: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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

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Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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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: Find the point of the intersection of the plane P: 2x - 3y + 4z + 14 = 0 and the line L:r = 1 – t,…

A: Given the equation of line and plane  2x−3y+4z+14=0x=1−ty=1+tz=2+3t

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

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Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: Find the point in which the line through the origin perpendicular to the plane 2x – y – z = 4 and…

A: We have to find the point in which the line through the origin perpendicular to the plane 2x-y-z = 4…

Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Find an equation of the plane. The plane that contains the line x = 3 + 2t, y = t, z = 6 - t and is…

A: We will find the equation of planes.

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

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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…

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Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

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: Consider the line L1 : ¤ = 3t, y =1+t, z=4+ 5t, and the plane II1 : -3x + y – 2z= 9. a) Find the…

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

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Q: Find an equation of the plane. The plane that contains the line x = 3 + 2t, y = t, z = 9 – t and is…

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Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Q3/ Find the plane determined by the interseetiny Lines L X=1-2t, , 3-st,,そニ-2+t, La.Xe-3+t2)…

A: To find equation of plane we need to first find point and direction ratio of lines. Then find…

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

A: We have to find the equation of the plane containing the line x=3t, y=2−4t, z=1+t and parallel to…

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

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

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

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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 at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: Find an equation of the plane. The plane that contains the line x = 2 + 2t, y = t, z = 6 − t and is…

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Q: Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t…

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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: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

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Q: Find the distance from the point Q to the plane p. Q= (0, 0, 0), p with equation x - 2y + 2z = 1

A: GivenQ=0,0,0p:x−2y+2z=1

Q: Q2. A. Show that the plane 3x +y- z = 9 and the line {x 2,y =-1+ 3t,z 1+ 3t} are parallel, then find…

A: Answer

Q: Determine the Cartesian equation of a plane that is perpendicular to the plane x - 2y + z = 6 and…

A: Given : A plane x-2y+z=6 and which contains a line -x+2-3=y+1=z+12  To find: The Cartesian equation…