Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y + 4z = 0. Find the z coordinate of the point of intersection of L and the plane 7x – 4y + 2z = 16

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-7,0,1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-4,0, 1) and is perpendicular to the plane x + 2y +…

A: Please refer the attached image for complete solution.

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let p be a plane which contains the point Q(1,2,3) and the intersection line of the planes: 2x+3y-…

A: Concept: 1. The equation of plane passing through the line of intersection of the given planes…

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: Let L be a line which passes through the point (-8,0, 1) and is perpendicular to the plane a + 2y +…

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Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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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: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane r + 2y +…

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Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: Find the plane that contains the point (0, 1, 2) and the line x = 1- t,y = 2 + t,z = 4 + 3t.

A: Here I am attaching image so that you understand each and every step.

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Let L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane r + 2y +…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

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Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane r + 2y +…

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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: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

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Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-8,0, 1) and is perpendicular to the plane z + 2y +…

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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: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane r+ 2y +…

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Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane x + 2y…

A: Direction ratio of Line is < 1,2,6> Write equation of straight line and solve it with plane to…

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A: Here we find the equation of line L and also find the intersecting point of line and plane.

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane r + 2y+…

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

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Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

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Q: Find the angle between the plane -2x +y-2z 0 and the plane generated by the points P1(0, 0, 0),…

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Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Let L be a line which passes through the point (-3, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Question 10

A: We have to find equation of plane that is parallel to the plane 6x-5y+8z+18 =0 and  the pale passes…

Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

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 point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane * + 2y +…

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Q: Find a plane through the points P(2,3,3), Q(6,4,0) and perpendicular to the plane 3x+y+2z= -3. (A…

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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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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.