The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: Find an equation of the plane. The plane that passes through (7, 0, −4) and contains the line x = 3…

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Q: Locate the point of intersection of the plane 2x + y−z = 0 and the line through (3, 1, 0) that is…

A: Our Aim is to locate the point of intersection of the plane 2x+y-z and theline through (3,1,0) that…

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

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

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

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: 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: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

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

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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 an equation of the plane. The plane that passes through the point  (1, −1, 1)  and contains…

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

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Q: Find an equation of the plane. The plane that passes through the point (-2, 2, 2) and contains the…

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Q: Find an equation of the plane. The plane through the point (5, –1, –6) and parallel to the plane 5x…

A: Given point is (5,-1,-6) and plane is 5x-y-z=3 find the equation of the plane which is parallel to…

Q: find the distance from the point to the plane. (0, 0, 0), 3x + 2y + 6z = 6

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Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: plane

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Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: Find the distance from the point (2, 1,−2) to the plane 6(x − 1) + 2(y − 3) + 3(z + 4) = 0

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Q: 52. The plane passing through the point P,(0, 2, -2) that is parallel to the plane 2x + y-z= 1

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Q: Find the general equation of the plane containing the point (2,-1,4) and normal to the line 2 I+3…

A: The equation of the line passing through the points x1,y1,z1 with direction ratios a, b and c is…

Q: Find the equation of the plane containing the point P(-2,4,3) and the line y+1 z+2 %3D 4 2 -3

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Q: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…

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Q: Find the distance between the point P(1, -2, 2) and the plane 2x + 3y + 6z - 1 = 0.

A: Formula to find out distance between point and plane is D= |ax+by+cz-d|/√(a^2+b^2+c^2)

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Where does the line through  (−3, 1, 0) and (−1, 7, 8)  intersect the plane  2x + y − z = −2?

A: Given : Points : ( -3 , 1 ,0) and ( -1 ,7,8) Plane : 2x + y - z = -2

Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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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: Find the distance from the point to the plane (2,-3,4) , x+2 y - 2 z = 13

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Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.

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Q: 25. Find an equation of the plane through the line of intersection of the planes x – z = 1 and y +…

A: Equation of a plane P that passes through the line of intersection of two planes P1 and P2 is given…

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

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

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: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

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Q: Find the point on the plane x - 2y + 3z = 12 that is closest to the point (0, 2, 2). (x, y, z) =

A: Just I have used the Lagrange multipliers method and find the required solution.…

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

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Q: Find an equation of the plane that passes through the line of intersection of the planes ( x – z = 1…

A: We have found the plane that passes through the line of intersection of the planes x-z=1 &…

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

A: To find The diatance between the point A(1,-1,3) and the given plane

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

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Q: An equation of a plane P passes through the point (0, 0, 3) and perpendicular to the line L:x =1 –…

A: Remember that the vector (l, m, n) is parallel to the line with parametric equationx=a+lt, y=b+mt,…

Q: Find an equation of the plane parallel to the liner= and containing the points (2, 2,-1) and (1, 0,…

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Q: Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

A: Parametric equation of a plane is: x,y, z=p+at+bs where a and b are the vectors parallel to the…

Q: Find an equation of the plane. The plane through the point (7, −2, −7) and parallel to the plane 9x…

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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: Find the point on the plane x+y+z%3D24 that is closest to the point (1,1,1).

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Q: Find an equation of the plane. The plane through the point (7, –2, –8) and parallel to the plane 6x…

A: We will solve the following.

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

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