The planes with the equations x + 3z = 12 and y - 5z = 10 intersect in a line. Find the equation for the line in the form (x, y, z) = (x1, yı, Z1) + n(a, b, c).

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

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Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: Solve for the distance from the point (-5, 4, 5) to the plane −x+4y−5z=4.

A: Given Plane: -x+4y-5z=4 and Point: (-5,4,5)

Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: write down the equation of the plane. The plane containing the point (1,-5,8) and orthogonal to the…

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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 through (-1 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

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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 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 exact value of the distance between the line of intersection of the planes 2x-y+2z 6,…

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Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

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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: Are the planes 2x + 4y - 2z = 1 and -3x - 6y + 3z = 10 parallel, perpendicular, or neither?

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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: Give the general equation of a plane which has point (1,2, -1) together with line with symmetric…

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Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x = −6+t,…

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Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

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Q: Find the equation of the plane con taining the points Р(4, -1, 3) Q(1, -2, -1) and R(1, 0, 8)

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: Find the equation of the plane containing the point (7,-2,-5) and is perpendicular to the line…

A: We have to find the equation of the plane

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 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 equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

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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: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: . Find an equation of a plane passing through the point (3, 4. 0) and containing the line of…

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

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Q: Find a plane containing the point (-4,-7,3) and the line of intersection of the planes - 2x + 7y +…

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Q: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

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Q: What is the distance from the point S(-2, 3, -2) to the line of intersection of the planes 2x + 3y +…

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

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Q: Find an equation of a line containing the point (1, 7, -3) and parallel to the yz- plane.

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Q: Find the equation for the plane through Po(-5, - 8,8) perpendicular to the following line. x= - 5-t,…

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Q: Find the equation of the line of intersection of the planes 2x+y-2z = 1 and x+2y-z = 4.

A: Planes are 3-dimensional spaces, that contains infinite lines. When two non-parallel planes…

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 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 a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

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

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

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

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