Find the symmetric equation of the line that is an intersection of the planes a: x-4y + 2z-2 = 0 and b: x + y-z-3 = 0

Q: The two planes r+y +z= 1 and r – 2y + 3z = 1 intersect in a line l.

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

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Q: A. Find the angle between the planes x+y+z 1 and x-2y+3z 1, and Find symmetric equations for the…

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Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t. Write…

A: Given:

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 points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: Draw the plane given by the equation. 3x + 2y − 6z = 12

A: To draw3x+2y-6z=12

Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

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Q: On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest…

A: Given planes, y+2z=12andx+y=6 Consider the point of intersection be x,y,z.

Q: @/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for…

A: Given equations of planes are x+y+z=1 and x-2y+3z=1 Here, a1=1,b1=1,c1=1 & a2=1,b2=-2,c2=3…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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

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Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

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Q: find the point in which the line with symmtric equation2-x =y-1/3 =z/4 intersect the plane 2x-y+z=2

A: we are given the line with symmetric equation:  2-x =y-13=z4 and equation of the plane is:  2x-y+z=2…

Q: Find the equation of the line given by the intersection of the following two planes: T1:-2x + 4y- z+…

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

A: Given equation of the lines are, x=6+t, y=-3-5t, z=5t The given equation of the lines can be written…

Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

Q: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

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Q: Find the equation of a plane through the intersection point of the lines r(t) = and 7(s)= where r, s…

A: The equation of plane is mainly given by the normal vector calculation. The normal vector to the…

Q: Find the equation where the planes 2x - 3y + z = 5 and x +y -z = 2 intersect. Write step by step.

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Q: Is the line x = 1 + 2t, y =-2 + 3t, z =-5t related in any way to the plane -4x - 6y + 10z = 9? Give…

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Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

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Q: Draw the plane given by the equation. x + y + z = 4

A: x+ y+ z= 4

Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: (a) Find an equation for the line of intersection between the planes z+3y-z = 2 and 2x –y+2z = 5.…

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Q: find the point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

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Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

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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: For the plane, 6x + 10y + 15z = 30, the values of the x-, y-, and z-intercepts are %3D 5, 3 and 2 3,…

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Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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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 the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

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 line where planes Q and R intersect. Q: x-3y+2z=1 R: x+y+z=-1

A: To calculate the equation of line from the point of intersection of the planes Q and R. Where, the…

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

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

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

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Q: Find the equation for the plane through Po(4,- 5,5) perpendicular to the following line. x= 4 + t, y…

A: ee

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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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.