Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x =-1 + t, y = 6 - 2t, z = 3t.

Q: Find the equation of the plane through (1,2,3) and parallel to the plane: x+y=-2-z

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

Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

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Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

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Q: Find the equation of the plane passing through the point (-1, 4, 0) perpendicular to the line L₁: x=…

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Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

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 an equation of the plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y =…

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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: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

Q: Find the equation of the plane that contains the line x=-1+3t, y=5+2t, z=2-t and is perpendicular to…

A: topic - equation of plane

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

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Q: Determine the general equation of the plane containing the point (1, 2, –1) and the line

A: The given equation of the line- 1-x3=y+23=z-3 It can also be written as follows- x-1-3=y+23=z-31…

Q: What is the equation of the plane through (-1,-1,-1) parallel to the plane x+ 2y + 3z = 9?

A: The vector normal to the plane ax+by+cz=d is ai^+bj^+ck^ . The plane parallel to this plane has the…

Q: Find the equation of the plane passing through (0,0,-4)and perpendicular to the line joining the…

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Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

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Q: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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Q: Find the equation of the plane through the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

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: Write the equation of the plane that is parallel to the xy-plane and passing through the point…

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Q: Find an equation of the plane that contains the point (2, 0, 3) and the line x =-1+t, y =t, z=-4+21…

A: It is given that the required plane contains the point 2,0,3 and the line x=-1+t,y=t,z=-4+2t. The…

Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

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

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Q: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

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

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Q: Find an equation of a plane through the point (0,−2,1) which is orthogonal to the line…

A: The equation of a plane passing through the given point is as follows.

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 equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Solve for the linear equation of the plane through the point (1,9,10)(1,9,10) and parallel to the…

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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: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find the equation of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Given, the plane contains the lines x = 3t, y = 1 + t, z = 2t and parallel to the line of…

Q: Find the equation of a plane passing through points (3,2,2), (1,0,-1) and parallel to the line…

A: Equation of plane is calculated as below:

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

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Q: Write the equation for the plane through the point P(- 4,4,2) and perpendicular to the line x =4+7t,…

A: Explanation of the answer is as follows

Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

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

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Q: Find the equation of the plane that passes through the point (1,0,-2) and contains the line with…

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

A: we have given x+2y+z=1  ...(i)x+y+2z=-1  ...(ii)solve it  2×(i)-(ii)x+3y=3   ...(a) this is equation…

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: Determine an equation for the plane that passes through the point (1, 2, –3) and is parallel to the…

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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 through the origin perpendicular to the plane 2x - y - z = 4 and…

A: Your line, perpendicular to the plane will have the slope of <2, -1, -1>, and passes through…

Q: Find an equation of the plane perpendicular to each of the planes z – y+z = 0 and 2r+y-4z–5 =0 and…

A: The given problem is to find the equation of plane perpendicular to each of the given planes and…

Q: Find the equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: Determine the cartesian equation of the plane having x-intercept of 2, a y-intercept of 5 and a…

A: To find the cartesian equation of the plane

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.