The planes with the equations x + 2z = 12 and y – 3z = 6 intersect in a line. Find the equation for the line in the form (x, y, z) (X1, y1, Z1) + n(a, b, c).

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: Find the distance from the point to the given plane. (1, -4, 6), 3x + 2y + 6z = 5

A: Given:   3x + 2y + 6z = 5     Point: ( 1 , -4 , 6 )

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t. Write…

A: Given:

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

Q: Find the equation of the plane that contains the point P(3,5,-1) and the linex = 4 - ty = -1 + 2t,z…

A: The plane contains the point P(3,5,-1) and the line x=4-t, y=-1+2t, z=-3t

Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

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Q: Find the distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

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Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

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Q: Find the equation for the plane through Po(- 4,8, - 3) perpendicular to the following line. x = - 4…

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Q: Find the equation of a plane bisecting the line segment joining (2,0,6) and (6,2,4) and…

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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 equation of the plane that contains the lines L,:x 3+5t, y = 6+2t, z = 7t and L2: x = 7t, y =…

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Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: Find the equation of the line that contains the point (1,–1, 2) and is perpendicular to the plane 2x…

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Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

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: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

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Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Find the line of intersection of the planes 2x+y-z=3 and x+2y+z=2. Find the equation of the plane…

A: Solution of part (a) in step2 and step3 and part (b) in step4.

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: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

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Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: Find an equation of the plane through (4, 5, 7) that is - 2 = 5t, y +3 = 10t, z = -5t. perpendicular…

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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 equation of Plane teter mined by the Lines Li. X = t-29 y = 2t+3 Z= +4 and Lz! X…

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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 general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

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Q: Find the general equation of the plane perpendicular to the line Z – 2 y+ 4 1- x = 3 and is 3…

A: This is a problem of vector algebra and geometry.

Q: Find the equation for the plane through Po(-7,- 4,7) perpendicular to the following line. x= -7+t,…

A: Solution: The objective is to find the equation for the plane through the given point and…

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: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

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

A: It is given that a point Q6,-2,4 and equation of the plane 2x-y+2z=4. Here, x1=6, y1=-2, z1=4  and…

Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Find the angle between the planes (x+y+za1)and. (x-24+32-1). And find the Symmetricequations for the…

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Q: Show that the plane whose intercepts with the coordinates axis are x = a, y =b, z c has equation :…

A: Consider an equation of plane as It is given that the intercepts of plane are x=a,y=b and z=c. So,…

Q: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Find the equation of the plane through (-6,5,-1) and is parallel to the xy plane

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Q: Find the distance of the point (3,8,2) from the line =22= measured parallel to the plane 3x + 2y- 2z…

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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 the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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Q: Find the equation for the plane through Po(-6,9,2) perpendicular to the following line. x = - 6 + t,…

A: Given that the point is P0(-6, 9, 2) and perpendicular line: x = -6 + t, y = 9 - 5t, z = 4t

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

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

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

Q: Find an equation of the plane through (-4, 3, –8) that is perpendicular to the line x – 2 = t, y +3…

A: Given line : x-2=t , y+3=2t ,  z=-tx-21=t , y+32=t , z-1=tx-21= y+32= z-0-1 comparing with standard…