Midpoint formula Prove that the midpoint of the line segment joining P(x1. y1- Z,) and Q(x,. Y2, Z,) is (x, + x, Y, + Y2 2 2 2.

Q: Isosceles trapezoid ABCD is centered at point K. Perpendicular lines m and n intersect at point k.…

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

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

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Q: 3. PQ lies in the stándard (x, y) coordinate plane. What are the coordinates of the midpoint of PQ…

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Q: Find a line that intersects the plane x+y+z=4 at only one point

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Q: Find the slopes of the surface at the given point in the x-direction and the y-direction. z = x2 -…

A: This question is related to slope of surfaces, we will solve it using given information.

Q: 3) Suppose plane P, contains the points A(5,0, –1), B(2,3, 2), and C(-2, 1, –4), and assume P, is…

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Q: A cariable straight line drawn through the point of intersection of the straight lines x/a+y/b=1 and…

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Q: (A) Find the angles between the planes 2 x + 2 y+ 2z = 3 and 2x- 2 y-z = 5 (8) Find the distance…

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Q: a) b) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in…

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Q: Coordinates of point which partitions a directed line segment AB at the ratio of a:b from A(x1,yı)…

A: Section formula we need to use

Q: . Parallelogram JKLM with vertices J(-1, 8), K(5, 6), L(7, -2), and M(1, 0); scale factor: k = 2,…

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Q: The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y - z =-4 in a point P. Find the…

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Q: Find the distance from the point (5, 5, 5) to the line x = 0, y = 5+ t, z = 5+t. Find the point P…

A: Explanation of the answer is as follows

Q: Parametric equations for the line containing (3,-1,4) and (-1,5,1) are: O x = 1- t, y = 3 + 6t, z =…

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Q: Find equations for all the planes that intersect the y-axis at y =1 and the z-axis at z =2, and are…

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Q: How do you solve for square roots in fractions? Im suppose to solve the midpoint of the line joining…

A: Given formula is M = (x1 + x2)/2

Q: Disk Method y = x^(2)-2x, x-axis ; about the x-axis

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Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, 2, 3), 2x + y + 2z = 4 40.…

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Q: Calculate the distance between the points L= (-9, 8) and J=(-1, 1) in the coordinate plane. %3D Give…

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Q: Coordinates of point which partitions a directed line segment AB at the ratio of a:b from A(xyı) to…

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Q: Point F is 50 mm from a vertical straight line AB. Draw locus of point P, moving in a plane such…

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Q: etermine the equation of the plane tangent to the surface x2 + y² – z² = –1 at the point , 1, v3).

A: To find The equation of the plane tangent to the surface at the given point.

Q: 4. Using two methods find the point point P = (5, 4, 4) on the plane x +y + z = 4 nearest the %3D

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Q: ation of the plane.

A: Topic:-: geometry

Q: An equation of the straight line normal to surface x2 - y3 + z = 8 at the point P(2, -1, 3) on the…

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Q: Find the shortest distance from the point (1, 0, -2) to the plane x + 2y + z = 16. The distance from…

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Q: The line = (2, -1, -2) + s(1, 1, -2), sER, intersects the xz-plane at point P and the xy-plane at…

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Q: Steepest ascent on a plane Suppose a long sloping hillside is described by the plane z = ax + by +…

A: Given function fx,y=ax+by+c is differentiable. Obtain the gradient.…

Q: 3. PQ lies in the standard (x, y) coordinate plane. What are the coordinates of the midpint of PQ if…

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Q: The line through the point (0, 14, – 10) and parallel to the line x= -1 + 21, y = 6 – 31, z = 3 + 9t…

A: If the line is parallel to the line x = -1 + 2t; y=6 -3t and z=3 + 9t, then the line is parallel to…

Q: Find the point at which the line x = 2 – t, y = 1+ t, z = 4t intersects the plane x - y + 3z = 11.…

A: Given,

Q: 17. projection of the line Find the equation of the 3x-y + 2z-1=0 = x +2y-z-2 on the plane 3x +2y +…

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Q: HOME WORK: find the distance from the point s(1.0.-1) to the plane -4x +y+z = 4

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Q: Va+ ド+で Find the distance between the point (0, 1,5) and the plane 3r + by – 2z-5 0.

A: topic - distance of point from plane

Q: Parameterize the curve of intersection of the surfaces so that the direction is clockwise when…

A: Note: According to our guidelines We’ll answer one of the question since the exact one wasn’t…

Q: Find the point at which the line meets the plane. x=3 + 3t, y = 4 + 5t, z = - 3+4t; x + y + z = 4…

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Q: Find the coordinates of the point. The point is located nine units in front of the yz-plane, eight…

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Q: Find the point P where the function f(x, y, z) = x¹y¹z7 reaches the maximum value for x, y, z ≥ 0 on…

A: Given the function fx,y,z=x4y4z7 reaches the maximum value for x,y,z≥0 on the unit sphere x2+y2+z2=1

Q: 2. Given point P = (1,2,1) and Q(3,3,0) Find b) the coordinates of the point M, where line L meets…

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Q: (b) Find the points in which the required line in part (a) intersects the coordinate planes. point…

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Q: Calculate the distance between the points J=(-2, 0) and P=(6, 6) in the coordinate plane. Give an…

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Q: The Line whose edualion is (X + *y +Z=!) > (x -y +2Z+7 =0) intersecks the parametric Rind the X z…

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Q: Coordinates of point which partitions a directed line segment AB at the ratio of a:b from A(x.yı) to…

A: We have…

Q: Scoliosis is a lateral curvature of the spine that can be detected when a grid is superimposed over…

A: We have to find the coordinates of the points given to us so, for that we will measure the distance…

Q: Cone: x2 + y2 - z2 = 0, Plane: x + 2z = 4

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

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