Find the point at which the line (0, –3, 5) + t(4, –1,2) intersects the plane 4x + 4y – 4z = 0.

Q: Find an equation of the plane that is parallel to the plane x + 8y – 4z + 12 = 0 and contains the…

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

A: x = 4 − t,  y = 2 + t,  z = 3t;    x − y + 5z = 15 We need to find the point at which the line…

Q: Find an equation of the plane. The plane that passes through the point (-3, 1, 2) and contains the…

A: This question is related to planes. We will solve this question by using property of plane

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 plane determined by the intersecting lines. z = 1-t L1 x= - 1 +t y = 2 + 3t L2 x = 1- 4s y…

A: Given: L1  x=-1+t    y= 2+3t   z=1-tL2  x=1-4s   y=1+2s   z=2-2s To find equation of  plane by these…

Q: Find an equation of the plane determined by the points P(1,2,3), Q(2,0, 1), and R(0, –-1,1).

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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,…

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Q: Find an equation of the plane that is parallel to the plane x + 4y – 3z + 16 = 0 and contains the…

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Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

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

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Q: Find an equation of the plane that is parallel to the plane x + 3y – 8z + 18 = 0 and contains the…

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Q: Find a plane containing the point (-4,-4,6) and the line of intersection of the planes -x + 3y – 2z…

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Q: Find an equation of the plane. The plane that passes through the point (−1, 3, 2) and contains the…

A: given planes are x+y-z = 5, 4x-y+5z = 1 The equation of plane that contains intersection of planes…

Q: 3) Find an equation of the plane whose points are equidistance from the point (2, - 1,1) to the…

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: ....... Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane…

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Q: Find an equation of the plane. The plane that passes through the point (-2, 2, 2) and contains the…

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A: Find equation of line and put parametric value of (x,y,z) in plane and solve for x,y and z.

Q: A perpendicular line is drawn from point P(1,2,1) to the plane -2x+ 4z 8 and meets the plane at…

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Q: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: Find an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…

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Q: Find the point of intersection of the line through (1, -5, 1) and (5,-12, 6), and the plane given by…

A: we know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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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 point at which the line intersects the given plane: 5x = y/2 = z + 2 and 10x - 7y + 3z +…

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Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Find an equation of plane through the points pl (-1, 1, 1) and point of intersection of the plane 2x…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y+z=2…

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Q: Find an equation of the plane. The plane that passes through the point (−3, 2, 1) and contains the…

A: It is known that equation of a plane passing through line of intersectionof planes .…

Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

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: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: Find a plane containing the point (1,-8,-3) and the line of intersection of the planes - 3x – 8y +…

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Q: Find an equation of the plane through (-8, 4, –9) that is perpendicular to the planes 5x – y +z = 1…

A: Solution of question is written in below steps.

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x-y + z =…

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Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

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Q: Find the points of intersection of the line 6. = y+3= z 4 with the plane I+ 3y + 2z – 6 = 0. ОА(-10,…

A: We will solve the following.

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

A: This question is based on finding direction cosine using dot product as two perpendicular plane is…

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

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Q: of the

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

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Q: Find a plane containing the point (3,-7,8) and the tine of intersection of the planes-4z +4y + 4z =…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

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