2. The plane with equation: 7 = (1,2,3) + m(1,2,5) + n(1,–1,3) intersects the y- and z- axes at two points. Determine those two points.

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

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Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

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Q: Find the point at which the line (3, 4, 5) +t(1, -1, –5) intersects the plane -5x + 2y+ z = -86.

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Q: Find an equation of a plane containing the line r = (4, –5, –4) + t (–7, 8, –4) which is parallel to…

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Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: Find the standard equation of the plane that contains three points A(1,0,–1), В(2, 1, 1) and C(1, 2,…

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: (b). Determine the equation of the plane that contains the points P(1, –2,0), Q(3, 1, 4) and R(0, 1,…

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Q: The line : X - 3t, y = 1 - 2t, z = 2 - t is perpendicular to the plane: X - y - z = 1.[g]

A: Given that equation of line x=-3t ,y=1-2t ,z=2-t and equation of plane x-y-z=1To chaque the line and…

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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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: Find the intersection of the plane – 5x + 4y – 6z = – 267 and the line T(t) = (6, – 7,6)t + (1, – 7,…

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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: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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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 an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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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 -12…

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

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

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

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

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Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

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: (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: Determine the equation of the plane that contains the points P(1,−2,0), Q(3,1,4) and R(0,1, -2)

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Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

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: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

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Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: 4-) Find the a Cute augle between the liue joning the two Points ACY2,3),B(5,1,7) , and the Plane…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

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Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: Given, The line x = -2,  y = 4+2t ,  z = -3+t   We have to find the points of intersection of line…

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 through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

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Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

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Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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