I don't need any graphical explanation, just the work to solve works and I can figure it out from there:   a. Find an equation of the plane that passes through (3, 2, -1) and contains the line l(t)= (-t, 2, 3+t), t is within the set of real numbers   b. Find the (perpendicular) distance between the point (3, 2, 0) and the plane through the origin spanned by v= (2,4,0) and w= (0, 1, -1)

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: what is the equation of the plane parallel to the xy-plane and passing through the point  P0=(1    0…

A: We can write the equation of plane in general form and satisfies by given point

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: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

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Q: Find the equation for the plane through Po(7.- 3. - 1) perpendicular to the following line. x=7+t,…

A: Ans     equation  of  line          x=7+t,   y=-3-3t,  z=-2t  or   x-71=y+3-3=z+0-2

Q: Find the equation of a plane through the point (- 1,1, 3) and orthogonal to the line ( x(t) = – 7 –…

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Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: Find the general equation of the plane π  that passes through the origin and is perpendicular to the…

A: Suppose a plane passing through the points x1,y1,z1 and a vector perpendicular to the plane is…

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

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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: Find the equation for the plane through Po(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

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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: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line x-1=, z=-23,…

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Q: Find the distance from the point (-2,0,3) to the plane given by the equation 3x+4y 5.

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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: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets…

A: Given that the line is passing through origin so ro = (0,0,0) and perpendicular to the plane 2x – y…

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: 286. Find the general equation of the plane that passes through the origin and is perpendicular to…

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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: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

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Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

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Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

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Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line X-1=と+2 3…

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Q: Find the equation of the plane through the point P = (3, 2, 5) and parallel to the plane a + 3y+ 3z…

A: Given: Line is parallel to x+3y+3z = 5 Equation of the plane parallel to the plane x+3y+3z = 5 is…

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: Consider the line L1 : ¤ = 3t, y =1+t, z=4+ 5t, and the plane II1 : -3x + y – 2z= 9. a) Find the…

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Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x…

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is…

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 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: Determine the general equation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

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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 distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

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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: . 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 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 an equation of the plane that is passing through the point and is perpendicular to the line L.…

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Q: Find the equation of the plane through the origin that is parallel to the plane 4.r – 2y+ 7z +12 = 0…

A: Consider the general equation of a plane, 4x-2y+7z+12=0 the normal vector of this plane will be…

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

A: ee

Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

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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.