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

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: At the point of intersection the point will satisfy the equation of both line and the plane. So…

Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute the…

Q: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6?

A: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6? Given x, y, z in…

Q: Calculate the distance from the point (4,−2,7) to the plane x−3y+5z=−8.

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Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

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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: Find the point of intersection between the line x+2/6 = y - 3 = z/3 and the plane x + 2y – 4z = 0.

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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 distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0.

A: Given Line is x=1+t,y=2t and z=-3t  And Given plane is x+y-z=0

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 intersection of the plane 4x – 6y – 7z = 10 and the line r(t) = (- 8, – 3, 3)t + (4, 1, 5).…

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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: At what point does the line: L: x=-1, y= 10 + 31, z= 4 +3t im plane 1:x- 2y + 5z + 16 = 0?

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Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

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Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

Q: Find the distance between the parallel planes – 2x + y + z = 0 and Edit 10x – 5y – 5z – 26 = 0. -

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Q: find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Is the line x = 4 + 2t, y =-t , z=-4t - 1 parallel to the plane 3x + 2y + z = 7 ?

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Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

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Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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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: Where does the line through (1,0,1) and (4,-2,2) intersect the plane x+y+z=6?

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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 the angles between the planes 5x + y - z = 10, x - 2y + 3z = -1

A: Solution -  We have equation of two planes -  Plane 1 -…

Q: The line x=4+2t, y=-t, z=-1-4t is parallel to the plane 3x+2y+z=7 FO

A: Direction cosine vector of the line is: L=2,-1,-4 and normal vector to the plane is N=3,2,1.

Q: Find the point at which the line intersects the given plane. x = 3 - t,   y = 3 + t,   z = 2t x - y…

A: Substitute the line equation in the plane equation

Q: Find an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

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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: find the point in which the line meets the plane x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6

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Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ < t < ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

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

A: Given:The point (1, –4,4) and the equation of the plane –2x–4y+3z=5.The distance from the point…

Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is: O…

A: Here the two equation are: x+2y+z=1x+y+2z=-1

Q: Find the distance between the parallel planes −3x+y+2z=−4 and 6x−2y−4z=1?

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Q: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

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

A: Given, The equation of line x = 1 + 2t, y = 1 + 5t, z = 3t and the equation of plane is x + y + z =…

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 point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

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Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

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Q: Does the line given by x = 9 + 21t, y = - 7, z = 12 - 11t intersect the xz - ?plane yes No

A: As per bartleby guidelines we only give first one question answer.

Q: Find the intersection of the plane 3x – y + 2z – 3= 0 and the line

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Q: find the distance from the point to the plane. (2, 2, 3), 2x + y + 2z = 4

A: We have to find the distance from the point (2,2,3) to the plane 2x+y+2z=4

Q: Find the plane determined by the intersecting lines. y = 2+ 4t L1 x= - 1+2t z = 1- 2t L2 x= 1-4s y =…

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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