cquation Of uIe HnC U Q2: Are the plane 2x-y-4z = 10 and the line {x = 2+ 4t, y = 5- 2t, z = -8t} parallel or いbioGし orthogonal? Gudı (1

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

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Q: Q5/ find the equalion of bhe plane that Condains the Line: x-!= +!2= and the Point A(5,1,) %3D 2.

A: See the attachment

Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

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Q: Find the point at which the line (3, 4, 5) +t(1, -1, –5) intersects the plane -5x + 2y+ z = -86.

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Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y+ 3z 9? (a) x -…

A: To find the equation of a plane through (-1,-1,0) parallel to the plane x+2y+3z=9

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 a plane through the points P(4,-1,2), Q(6,2,1) and perpendicular to the plane -x+y+z=3

A: Given: Points, P(4, -1, 2) Q(6, 2, 1)

Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

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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: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z 3 -12…

A: The point of intersection will satisfy the line as well as the Planes equation.

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

A: We have to find equation of ohm plane

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Determine the Cartesian equation of the plane that contains the line = (7,2,-1)+ a(4,5,1) and…

A: Given problem:- Determine the Cartesian equation of the plane that contains the line = (7,2,-1) +…

Q: a)What is the distance between the point A(3,1,-1) and the plane 4x + 4y +7z +2=0 ? b) Find the…

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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 and the line. (If an answer does not exist,…

A: Given: 2x+5y=-7; x-38=y2=z-714 Let, x-38=y2=z-714=t ⇒x=8t+3; y=2t; z=14t+7

Q: Find an equation for the plane through point (-2, –3, 3) parallel to the plane 0x – 9y – 1z = 44. An…

A: The given point is -2,-3,3 and the plane is 0x-9y-1z=44.

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

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Q: cquation o Uie Ie V Are the plane 2x-y-4z = 10 and the line {x = 2+4t, y = 5- 2t,z =-8t} parallel or…

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Q: a) Find the point of intersection between the lines x = 2t, y =t+ 2, z = 3t – 1 x = 5k – 2, y = k+…

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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 the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: Find the point at which the line meets the plane. x= -3+5t, y= -2+4t, z 3t, x+y+z= -5 The point is…

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Q: ans ) Find the lengthaf the Projection of the line jeining (-1,2,) ane -19 2) on the Plane…

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Q: 4. Calculate the distance between the point Q(3, 1, 7) and the plane 2x-6y-z=3. Don't use a formula.…

A: Given point Q(3,1,7)and the plane 2x-6y-z=3. The objective is to find the distance between the point…

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (-1,-6, 5)…

A: Given: Equation of line as, l:(x,y,z)=(-1,-6,5)+n(1,3,-2) And the equation of the plane is given as…

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y - z = -2? (x, y, z)…

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Q: Q1-)A-) Find the distance from the point (0,1,1) to the line of intersection of the planes : x + 2y…

A: Given: A) Point (0, 1, 1) and the planes x + 2y + z = 1, x - y + 2z = -8. B) Vertices of triangle…

Q: Where does the line through (-3, 1, 0) and (−1, 3, 8) intersect the plane 2x + y − z = -2? (x, y, z)…

A: Given the points (-3,1,0) and (-1,3,8) and the plane 2x+y-z=-2

Q: Sfor fig shuwn, find the plane using algebric methorde C0,0,3) Cり,) ×

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Q: 4. What is the equation of the plane through (1 ,2,3) parallel to the plane x- 2y + 3z = 9? (a) x 2y…

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Q: Find the point at which the line meets the plane. x=3 + 3t, y = 4 + 5t, z = - 3+4t; x + y + z = 4…

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Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (а) х…

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Q: a) Find the angle between the planes 2x+ 5y -6z 0 and 3x+ 6y + 8z= 0 b) Find the distance between…

A: Given: a) Planes 2x+5y-6z=0 and 3x+6y+8z=0. b) Planes 4x-y+2z-6=0 and 8x-2y+4z+6=0. To find: a)…

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 point of intersection of the line L given by {(x, y, z) = (5,-1,1) +r(-3,-1,-5) rER} with…

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Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

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Q: 6. Determine the point of intersection of the line l: = [-6,9,–1] + t[-2,3,1], t € R. and 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: . Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z =…

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Q: Find the intersection of the line 1₁: x-6 2 || y+2 1 with the plane p: x-6y - 2z - 10 = 0

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Q: Q4. Find the angle between the plane -2x + y- 2z 0 and the plane generated by the points P1(0, 0,…

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Q: 5. Cakculate the distance between the point (3. 1. -2) and the plane 2x + y - z+1-0 O 10 /14 O -10…

A: Find the distance between point and plane?  Value of k for det A= -4

Q: 25. Find the intersection of the line [x, y, 2] = [1,4, – 2] + 1(1, – 1,3] and the plane 2r – 4y +…

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Q: Po (2,1,-1) and perpendicular to the line of Find a plane that passes through intersection of the…

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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…