Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist, enter DNE.) = 10 X - 2 y z - 5 3x + 4y = -7, 6. (x, y, z) = Determine whether the line lies in the plane. The line ---Select--- lie in the plane.

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: Find an equation of the plane.  The plane through the point (2, 0, 5) and perpendicular to the line…

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Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Q4. Find an equation of a plane that contains the line x=t, y=1+2t, z=2-t.

A: We have to find the equation of plane .       According to our guidelines ,we cannot solve all…

Q: Q5) the value of the constant a for which the line x=2+t,y=2+3t,z=3+t and the plane ax+y-2z-7=0 are…

A: We will use definition.

Q: Find the equation of a plane through the point (- 1,1, 3) and orthogonal to the line ( x(t) = – 7 –…

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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 point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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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,…

A: 4x + 5y = 10 x-1/5 = y+1/-4 = z-7 now make x in y form x-1/5 = y+1/-4 -4x +4 = 5y+5 4x =-5y -1 put…

Q: Q2/ Find the equation of the plane through the point (2, 4, 5) perpendicular to the line: X=5+t,…

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

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Q: Find the intersection of the line and the plane. x + y + z = 14, r(t) =〈1, 1, 0〉+ t〈0, 2, 4〉

A: Given that, The equation of the line is: x + y + z = 14 And, the equation of the plane is:  r(t)…

Q: Find an equation of the plane. The plane through the point  (6, 0, 1)  and perpendicular to the line…

A: Given, The plane through the point (6, 0, 1) and perpendicular to the line x = 7t, y = 8 − t, z = 5…

Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

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

A: A line will lie in a plane if any two points on the line also lies in that plane. As we know between…

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

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Q: Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane :2x-2y-2z=3 is

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Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

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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,…

A: A detailed solution is given below

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(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 the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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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,…

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 the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

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Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

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

A: Given that:                    The line with equation:      x=83+2t, y=-2t, z=1+t     & Plane:…

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

A: This question is related to plane and lines, we will solve it using given information.

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

A: Given:   Plane→   2x+3y = 10  Line→       x-1 3= y+1-2 = z-9

Q: find the point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

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Q: 4. Find the equation of the plane that contains the intersecting lines a = 4 +t1, y = 2t1, z =1-3t…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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

A: Given line, x-14=y2=z-36And given plane3x+4y=-7Any  point on the line isx-14=y2=z-36=tx-1=4t,y=2t,…

Q: Find the intersection of the line and plane: x + 3y – 4z = 18, r(t) = (-3, 2, –2) + t(-3, 2, – 1)…

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Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2-2t meets the !3! plane 6x + 3y- 4z -12

A: Here we have to find the point at which the line x=2, y=3+2t, z=-2-2t meets the plane 6x+3y-4z=-12…

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

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 an equation of the plane. The plane through the point (4, 0, 1) and perpendicular to the line…

A: Given that, Let, the required equation be, lx-a+my-b+nz-c....(1) The required plane passing through…

Q: find the point in which the line meets the plane x = 2, y = 3 + 2t, z = -2 - 2t; 6x + 3y - 4z = -12

A: The equation of plane is 6x + 3y - 4z = -12. The coordinates of the line is x = 2, y = 3 + 2t, z =…

Q: Find an equation of the plane. The plane through the point (-3, 7, 10) and perpendicular to the line…

A: Given:- The plane through the point (-3, 7, 10) and perpendicular to the line x = 5 + t, y = 2t, z =…

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: Q1. Find the equation of the plane determined by the lines : L₁: (x = -2+1, y = 21 +3₁ Z=4-1), L₂:…

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Q: Find the​ point, P, at which the line intersects the plane. x=-5-6t , y=9-8t , z=8+7t ; 2x-4y-9z=-2…

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

A: Given line x-38=y2=z-714=tAny point on the line is of the form,x=3+8t,y=2t,z=7+14t,Put…