Consider the plane P with equation -2x+2y-z =3 and line L with equations x= -3-3t y = 3+7t z= 21 Find two distinct points Qj and Q2 on the line L at distance 3 to the plane P. Q1 =(0,0,0) Q2 = (0,0,0)

Q: Find an equation of the plane that is parallel to the plane x + 8y – 4z + 12 = 0 and contains the…

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Q: Find an equation of the plane that is parallel to the plane x + 2y – 4z + 16 = 0 and contains the…

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Q: Find the distance between the point (1, 0, 2) and the plane 2x – 3y + 6z = 6.

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Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z12 20. (2,8,4) and 2x+…

A: a) given point is (0,0,0)  plane is 2x+3y+z=12 find the distance between the point and the plane  b)…

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 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: 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: Find the distance between the point (-1, 1,-1) and the plane 3x - 5y + 2z = 12

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Q: Consider the planes of equations −y+z−2=0 and x−y=0. a) Show that the planes intersect. b) Find…

A: We can solve this using definition of intersection of plane

Q: Find the distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

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

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Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

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: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the…

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Q: Find a plane through the points P1(1, 2, 3), P2(3, 2, 1) and perpendicular to the plane 4x - y + 2z…

A: The given points and the plane are,

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

A: Given problem:- Determine the general equation of the plane π passing through the point P(1, -4,-5)…

Q: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

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 general equation of the plane containing the point (2,-1,4) and normal to the line 2 I+3…

A: The equation of the line passing through the points x1,y1,z1 with direction ratios a, b and c is…

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…

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Q: Find the distance between the point P(1, -2, 2) and the plane 2x + 3y + 6z - 1 = 0.

A: Formula to find out distance between point and plane is D= |ax+by+cz-d|/√(a^2+b^2+c^2)

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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

A: See the attachment

Q: Find an equation of the plane. the plane that contains the line x = 2 + t, y = 3 - t, z = 5 - 3t and…

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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: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

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: 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: Write the equation for the plane. The plane passing through the point Po(- 3,1,7) that is…

A: Given that, the point is P0-3,1,7 and the line is x=-1+6t,y=2-5t,z=3+4t. Note that, the plane is…

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

A: Your line, perpendicular to the plane will have the slope of <2, -1, -1>, and passes through…

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 that is parallel to the plane x + 2y – 7z + 15 = 0 and contains the…

A: A detailed solution is given below.

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: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

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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: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

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