Q3/ For the given vertices A, B, C and D of the parallelogram, Find the angle at B and the polar coordinates of the point where the diagonals intersect. A (0,0), B (7,3), C(9,8), D (2,5).

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: 2 -10 -8 2 4 8. 10 -2 R S. -4 -6 -8 10 GPS #3 $4 % 2 4 6 7. 6 2. 4. 6,

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Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: Rhombus WXYZ with vertices W(1, 5), X(6, 3),Y(1, 1), and Z(-4, 3) in the x-axis W'

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Q: Find parametric equations for the line that passes through the points P(-3,7,9) and Q(4, 1, -5).

A: The given points are P-3,7,9 and Q4,1,-5. The line containing the point x0,y0,z0 and parallel to the…

Q: Graph the Image of polnts A and B after a reflection over the x-axis. UNI CLICK TO SELECT 10 POINT A…

A: The reflection of a point say A(x,y) over axis leads to the  new co-ordinates as A'(x,-y)  The x…

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

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Q: If quadrilateral ABCD was rotated 270 degrees counterclockwise about point D, what would be the…

A: Use coni method to find the rotation of point B after 270 degree rotation, zB'-zDzB-zD=cosθ+isinθ…

Q: Find parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

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Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

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Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

A: Two planes are neither perpendicular nor parallel.

Q: Find the distance from the point to the plane. (2,5,6), у + 6z%30 The distance is

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3), C(5, 6), and D(2, 1): (x, y)- (x+2, y-6)

A: In Rhombus, A=(-3,-2)B=(0,3)C=(5,6)D=(2,1)

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

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Q: -4 2 -10 -8 -6 -4 -2 2 10 -2 U -4 -8 -10 W 00 6, 6,

A: solution given below..

Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Find the angle between the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5.

A: Given equations of the planes3x-6y-2z=15 and2x+y-2z=5we have to find the angle betweenthem θ

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

A: a. The points are A0,-40, 0 and B (40, 0,-20) Obtain the distance AB:…

Q: ectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,-4), R(6,-2,-5), and is…

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Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below with…

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Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

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Q: Write the coordinates of the vertices after a rotation 180° counterclockwise around the origin. 10…

A: Given query is to find the the coordinates of the L,M,N after counterclockwise rotation of 180°…

Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: Graph each figure and its image under the translation with the given rule. Give the coordinates of…

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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: Points M,N,P, and Q connecting together produces a rhombus MNPQ with diagonals MP and QN of the…

A: A rhombus is a type of quadrilateral whose four sides are of the same length. The angles of a…

Q: Find the angle between the planes 3x-6y – 2z = 15 and 2x +y – 2z = 5

A: Recall: Vector method, cos θ=n1·n2n1n2 We have, n1=3i-6j-2k, n2=2i+j-2k

Q: Use the cross product to find an equation for the plane that passes thru the points (1, 2, 3), (4,…

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Q: Find the distance the point P(2,0,1) is form the plane 3x – 6y + 2z = 15. -

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Q: What will be the new coordinates of the triangle with vertices A(0,1),B(1,2) and C(1,0) when : i) it…

A: given coordinates of a traingle ABC A(0,1),B(1,2) and C(1,0) what will be the new coordinates of…

Q: 4. Calculate the distance between the point Q(3, 1, 7) and the plane 2x-6y-z=3. Don't use a formula.…

A: Given point Q(3,1,7)and the plane 2x-6y-z=3. The objective is to find the distance between the point…

Q: 4) What rule and unit vectors are used to do 3-dimensional graphing? Graph the plane, R = 3x-2y +62…

A: To Explain: The rules of plotting the plane R: 3x-2y+6z=4.

Q: Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=0

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Q: Find the centroid of the triangle if the vertices are  (0,0) , (4,0) and (0,6)

A: Given points are         0,0,4,0,&0,6      And centriod G ?      centriod G= x1+x2+x33…

Q: Find // (4x + 5y)dA where R is the R parallelogram with vertices (0,0), (-3,1), (2,4), and (-1,5).…

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Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: 3. parallelogram ABCD with vertices A(1, 6), B(4, 5), C(1, –1), and D(-2, 0); translate by (3, -2)…

A: To get the coordinate of translation image we add vector and coordinate of original image.

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: -) Find the distance from the point (4, 22, 6) down to the ry-plane. ) Find the distance from the…

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Q: Find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5 Thank you.

A: To find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5

Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

Q: Find parametric equations for the line segment joining the points (-6, 7) and (4, 5). x=7-2t, y…

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Q: Find the coordinates of the vertices after the prism is rotated counterclockwise about the z-axis…

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Q: Let P be the parallelogram in the plane with vertices (0,0), (1,2), (1, 1), and (2, 3). Find SSp¤…

A: We need to find integral.

Q: The endpoints of AB are A(4,3) and B (1,1). What are the coordinates of A" after the image has been…

A: Coordinates of A.

Q: Q4. Find the angle between the plane -2x + y- 2z 0 and the plane generated by the points P1(0, 0,…

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Q: ■ Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3)…

A: Distance of a point from plane