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 Z=ー16, then A+B+C=

Q: Find the equation of the plane through (-1,4,2) and containing the line of intersection of the…

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Q: Find the distance from the point (-5, -1, -3) to the plane 5x + 3y + 2z = 1

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Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

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: The plane passes through the point (18, -16, 9) and contains the line given by = = z . 1.

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Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: Determine the point on the plane 4x- 2y + : = 1 that is closest to the point (-2,-1,5)

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Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

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Q: write down the equation of the plane. The plane containing the point (1,-5,8) and orthogonal to 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 point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

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Q: Find a line passing through (−2, 5, −3) and perpendicular to the plane 2x − 3y + 4z + 7 = 0.

A: we have to find a line passing through (-2,5,-3) and perpendicular to the plane 2x-3y+4z+7=0   as we…

Q: The line through the points (−3, 8,−4) and (1, 0, 8) intersects the yz-plane at _____.

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

Q: Find the exact value of the distance between the line of intersection of the planes 2x-y+2z 6,…

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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 consisting of all points that are equidistant from (1, 0, -2) and (3,…

A: Let's assume the coordinates of all the points which are equidistant from a points (1,0,-2) and…

Q: Find an equation of the plane consisting of all points that are equidistant from (0, -5, 2) and (-5,…

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

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Q: Give the general equation of a plane which has point (1,2, -1) together with line with symmetric…

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Q: Find an equation of the plane consisting of all points that are equidistant from (2, 4, 2) and (-2,…

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Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: Find the distance between the parallel planes.2x + y - 2z = 0 and 2x + y - 2z = 5

A: The given parallel planes are 2x+y-2z=0  and  2x+y-2z=5. The objective is to find the distance…

Q: Find the equation of a plane consisting of all points that are equidistant from (5,5,-1) and…

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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 distance from the point (-3, 4, -1) to the plane 5x−4y−5z=−3.

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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…

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

A: For solving This question I found direction cosine using dot product as two perpendicular plane is…

Q: Which of the points A(-4, 0, -1). B(3, 1, -1), and C(2, 4, 6) is closest to the yz-plane? Which…

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Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

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Q: Find the equation of the plane containing the point (7,-2,-5) and is perpendicular to the line…

A: We have to find the equation of the plane

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: Find a plane containing the point (-4,-7,3) and the line of intersection of the planes - 2x + 7y +…

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Q: Determine the equation of the plane that contains the points (3, 4, 1), (1, 7, 1) and (-1, -2, 5)

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Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: What is the distance from the point S(-2, 3, -2) to the line of intersection of the planes 2x + 3y +…

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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 equation of a plane passes through (1, 2, 3), (3,2,1) and (-1, -2, 2) ○ 4x - 3y + 4z = 10…

A: This question is based on finding equation of plane that passes through 3 points.

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 the equation for the plane through Po(-5, - 8,8) perpendicular to the following line. x= - 5-t,…

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Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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

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Q: Write the equation of the plane passing through point (3, 8, 3)| that is parallel to the xz- plane..

A: Given: A plane passes through (3, 8, 3) and is parallel to the xz-plane. To Find: Equation of plane

Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

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: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…

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

A: Find the equation of line and then find its intersection with the plane

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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