The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

Q: Find the distance from the point (-5, -1, -3) to the plane 5x + 3y + 2z = 1

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Q: 4] Find the equation of the plane that contains the point (a, 0, 0), (0, b, 0) and (0, 0, c).

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Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

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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: Determine the point on the plane 4x- 2y + : = 1 that is closest to the point (-2,-1,5)

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Q: Find the general equation of the plane containing the points P1(-1, 2, 0), P2(3, 4, -1), and P3(-2,…

A: Given points are  P1(-1,2,0)  P2(3,4,-1) and P3(-2,-1,0)

Q: Find an equation of the plane that passes through the point (1,-1,1) and contains the line of…

A: Let P=(1,-1,1) and n1=<1,1,-1> ,n2=<2,-1,3> The vector a for the line of intersection,…

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

A: Follow the procedure given below.

Q: Find a line passing through (−2, 5, −3) and perpendicular to the plane 2x − 3y + 4z + 7 = 0.

A: we have to find a line passing through (-2,5,-3) and perpendicular to the plane 2x-3y+4z+7=0   as we…

Q: Find a plane containing the point (-4,-4,6) and the line of intersection of the planes -x + 3y – 2z…

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Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: Find the equation of the plane containing the point (- 7, – 8, 0) and parallel to the plane 6x + 8y…

A: To find equation of a plane we use Concept of Direction Ratio of the given parallel plane.

Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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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 an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: The equation of plane through the origin and parallel to the plane 2x+ 5y – 4z = 8 is 2x + 5y – 4z =…

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Q: find the lineof interseetion of the plane -2x + 79 -2= 24 given by 3x t6y-52=-3 the plane

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

Q: Find the intersection of the line and the plane. 2x + y = 3, r(t) =〈2, -1, -1〉+ t〈1, 2, -4〉

A: We have to find the intersection of the plane 2x+y=3 and the straight line r(t)=2,-1,-1+t1,2,-4

Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

A: Find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

Q: Find an equation of the plane that is parallel to the y-z plane and that passes through the point…

A: NOTE: Refresh your page if you can't see any equations. . the equation of any plane parallel to the…

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

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Q: Find the distance from the point (-3, 4, -1) to the plane 5x−4y−5z=−3.

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Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: The equation of plane through the origin and parallel to the plane 2x +5y-4z = 8 is 2x + 5y- 4z = 0.

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Q: Find the distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: Find the distance from the point (-5, –13,6) to the plane –9x + 3y – 8z = -67. Distance is ...

A: Given:            point a(-5,-13,6)=(x0,y0,z0)            plane equation is -9x+3y-8z+67=0we know…

Q: Find the distance between the parallel planes P1: 2x – y+2z + 6 = 0 and P2: 6x - 3y+ 6z – 18 = 0 3y…

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Q: Find the distance between the point P(-1, 2, -1) and the plane 2x + 6y - 9z + 1 = 0.

A: Use formula to calculate distance

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 line of the intersection of the planes -2xr+3y+7z+2=0, x+2y-3z+5=0.

A: We have two equations in three variables. To find the line of intersection of these planes, we fix…

Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

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Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

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: The plane passes through the points (4, 3, 1) and (4, 1, -6) and is perpendicular to the plane 8x +…

A: SOLUTION-

Q: Find a plane containing the point (1,-8,-3) and the line of intersection of the planes - 3x – 8y +…

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Q: 4] Find the equation of the plane that contains the point (a, 0, 0), (0, b, 0) and (0,0, c).

A: As per our company guidelines we are supposed to answer only one question kindly post other parts in…

Q: Find a plane containing the point (2,-1,3) and the line of intersection of the planes 5x + 7y – 6z =…

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Q: Find the equation of the plane through Po (2,-1,-1) and P1(1,2,3) and perpendicular to the plane…

A: Given: P0(2,-1,-1) and P1(1,2,3)  2x+3y-5z-6=0

Q: 4] Find the equation of the plane that contains the point (а, 0, 0), (0, b, 0) and (0, 0, c).

A: First find two vector and then take cross product which is normal vector  Now use equation of plane

Q: Determine the cartesian equation of the plane having x-intercept of 2, a y-intercept of 5 and a…

A: To find the cartesian equation of the plane

Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

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

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