Q1/ Find the distance between the point p(2,3,4) and the plane containing the following points A(0,0,1), B(1,0,0) and C(0,2,0)

Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: Find the distance between the point (1, 0, 2) and the plane 2x – 3y + 6z = 6.

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Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.

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Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z12 20. (2,8,4) and 2x+…

A: a) given point is (0,0,0)  plane is 2x+3y+z=12 find the distance between the point and the plane  b)…

Q: Find the distance from the point (2, –1, 5) to the plane 3x + 2y – 2z – 7 = 0.

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Q: Find the distance between the point (3,4,5) and the plane 2x + 4y 3z = 12.

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Q: Find a plane through the points P(4,-1,2), Q(6,2,1) and perpendicular to the plane -x+y+z=3

A: Given: Points, P(4, -1, 2) Q(6, 2, 1)

Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

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

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

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

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

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 a plane through the points P1(1, 2, 3), P2(3, 2, 1) and perpendicular to the plane 4x - y + 2z…

A: The given points and the plane are,

Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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

A: Please see the explanation below

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: Find an equation of the plane that is parallel to the y-z plane and that passes through the point…

A: NOTE: Refresh your page if you can't see any equations. . the equation of any plane parallel to the…

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

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Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: Where does the line through  (−3, 1, 0) and (−1, 7, 8)  intersect the plane  2x + y − z = −2?

A: Given : Points : ( -3 , 1 ,0) and ( -1 ,7,8) Plane : 2x + y - z = -2

Q: Find an equation for the plane consisting of all points that are equidistant from the points (1, 0,…

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Q: Find the distance from the point to the plane (2,-3,4) , x+2 y - 2 z = 13

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Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.

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Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

Q: Find the equation of the plane containing the point (4, -1, 3) that is parallel to the plane 2x - 3y…

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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: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

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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 the distance between the point P(-1, 2, -1) and the plane 2x + 6y - 9z + 1 = 0.

A: Use formula to calculate distance

Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

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Q: Find the distance between the point (3, −2, 4) and the plane 2x − 5y + z = 10.

A: Given: The equation of a plane is 2x-5y+z=10. To determine: The distance between the point 3,-2,4…

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: 4) Find the distance from the point (1, 2, – 1) to the plane 2x+y- 2z = 1.

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Q: Find an equation of the plane. The plane through the point  (8, −3, −3)  and parallel to the plane…

A: We know that two parallel planes have same direction ratios(i.e. the coefficients of x,y and z…

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

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Q: 4. Determine the equation of the plane passing through the point (1, -4, 3) and parallel to the…

A: We have to find an equation of the plane passing through the point (1, -4, 3) and parallel to the…

Q: between the point and the plane. 43. (1,−2, 3); 2x − 2y + z = 4

A: Given: The point is 1,-2, 3 and the equation of the plane is 2x-2y+z=4 To find the distance between…

Q: Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

A: Parametric equation of a plane is: x,y, z=p+at+bs where a and b are the vectors parallel to the…

Q: Find the distance between the point (3, -4, 2) and the plane 5x- 2y +z = 10.

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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: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

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Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

Q: Find the distance from the point to the plane. (3, 0, 10), 2.x + 3y + z = 2

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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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.