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

Q: write the equation of plane 4x-4y+2z+5=0 in the intercept form

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Q: Q2: Find the equation of the plane that pass through the point P(-1,4,2) and containing the line of…

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Q: Find the x-, y-, and z-intercepts of the plane. (If an answer does not exist, enter Di 4x - 5y + 2z…

A: for x intercept, y=z=0 for y intercept, x=z=0 for z intercept, x=y=0

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

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

A: To draw3x+2y-6z=12

Q: What is the y-coordinate of any point in the xz-plane?

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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: 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 intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

Q: Write the equation of the plane that contains the point P(1, 3, 5) and the line L: x = 4t, y = 6 +…

A: It can be solved using properties of plane.

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: 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: draw the plane given by the equation  12x − 6y + 4z = 6

A: To plot the graph of 12x-6y+4z=6, write the equation in terms of x and y for z and obtain…

Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

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

A: To find the equation of a plane passing through (2,0,1) and perpendicular to the line x=3t , y=2-t ,…

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: (50p.) l- Find an equation of the plane through (1,3,–2) and the line of intersection of the two…

A: Given that, P1 : x-y+z=1 P2 : x+y-z=1 and Point A(1,3,-2)   We have to find Equation of Plane…

Q: Determine whether or not the planes f1:   3x  –  y  + z – 2 =  0 f2:     x + 2y –  z + 1 =  0 f3:…

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Q: Find the equation that is perpendicular to y = x +3 and passes through the point (-3, -4). %3D Oy =…

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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: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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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: Determine whether the line L: = 3- 2t, y=4+ 2t, z = 5+ 2t. is parallel to the plane a-y+3z 7.

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

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

Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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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 line of intersection of the given planes. 4x + y – z = 0 and 2x - y + 3z = 4 y = 2 + t 2

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

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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: 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: Determine whether each point lies in the plane.  2x + y + 3z − 6 = 0 (a) (3, 6, −2)    (b) (−1, 5,…

A: Given- 2x+y+3z-6=0 To find-  whether each point lies in the plane and the points are (a) (3, 6, −2)…

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

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Q: . Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 2+8 L1 : 4 -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: Determine the points of intersection of the given line and the three coordinate planes. x =1+2,y…

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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 equation of a plane that contains the lines and - 2+5. O A 2x-y-22 = 42 O B. 2x y 2z -10 O…

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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

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.