Find the distance between each pair of points: а) (-3, —7) and (2, 5) b) (0, 0) and (-2, 6) с) (-а, —b) and (a, b) d) (2а, 2b) and (2с, 2d)

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

A: Given:   3x + 2y + 6z = 5     Point: ( 1 , -4 , 6 )

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

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Q: Solve for the distance from the point (-5, 4, 5) to the plane −x+4y−5z=4.

A: Given Plane: -x+4y-5z=4 and Point: (-5,4,5)

Q: The diagram shows the parallelogram-shaped component that attaches a car's rearview mirror to the…

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Q: Calculate the distance from the point P(9,4,3) to the line which contains points A(1,0,1) and…

A: we use  product rule to find distance between line and point

Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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

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Q: The midpoint of AB is M(-1, -5). If the coordinates of A are (3, –8), what are the coordinates of B?

A: A detailed solution is given below

Q: Find the distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

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Q: Use v=<3/5,4/5>,w=<-4/5, 3/5>, to verify the Parallelogram Law

A: The given vectors are

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: 11. X(3, 2), Y(3, -12) 12. A(-4, -2), В(4, - 1)

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Q: Find the coordinates of the point 7. of the way from A to B. 10 本y 10 8- B(t0,7) 6- 2- -> -6-4-2 -2…

A: Given P is a point 710 of the way from A to B .This implies that point P divides the line AB in…

Q: Find the distance from the point (3, -4, 2) to the yz-plane

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

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 from the point (3, 5, 1) to the line æ = = 0, y = 5 + 2t, z = 1+ 3t.

A: Given line x=0, y=5+2t, z=1+3t Therefore line passing through the point (0,5,1) and direction ratio…

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

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Find the distance from the point A to the line through the points B and C where A, B, d C have the…

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Q: if (u, v) and (s, t) are two distinct points in the plane, what is the distance between them?…

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Q: B) Find Duf of f(x,y.z) x + y? + 2? - 3 at point(1,1,1)in the direction of point (3,5,-3).

A: Take gradient at given point and take dot product with unit vector for directional derivative

Q: find the distance from the point to the plane. (6, 0, -6), x - y = 4

A: x1,y1z1=6,0,-6…

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

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: What is the distance between the points M(-3,1) and N(7,-3)?

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Q: Reflect the triangle over the line y=x with the rule (x,y)→(y,x) -8- 4- -8 -4 4 8 -4- --8

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Q: Find the distance from the point (-5, –13,6) to the plane –9x + 3y – 8z = -67. Distance is ...

A: Given:            point a(-5,-13,6)=(x0,y0,z0)            plane equation is -9x+3y-8z+67=0we know…

Q: Find the distance from the point (3, 2, 5) to the line 0, y = 2+ 2t, z = 5 + 2t.

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Q: Find the point P on the line y=6x that is closest to the point (74,0).  Type an ordered pair.

A: Given:The line y = 6x and a point (74,0).Let p be the point that is closest to the point (74,0). Let…

Q: the distance between point and our plane is (-3, 3, -2) and not (-3, -3, -2)?

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Q: Find the distance from the point (2, 1, 3) to the line x = 2 + 2t, y = 1 + 6t, z = 3

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Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: Consider the points P(-4, 1, 0, 3), Q(0, 3, 1, -4), R(-2, 1, 5, 0). RS PQ is parallel to Find the…

A: Given:- P=(-4,1,0,3) ,Q=(0,3,1,-4) and R=(-2,1,5,0) To find the point S in R4 whose third component…

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 the angle between two planes -3/2x- 6y+ z= 4 and 2x−y−1/2z= 7 , also find an equation for the…

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Q: Palocated at (8,-7), and Qslocated at (-4,-3) on the coordinate plane What coordinate represents the…

A: Mid point (x ,y) of (x 1 , y 1) and (x 2 , y 2) is given by x = (x 1 + x 2)/2 and y = (y 1 + y 2)/2

Q: Find the distance in between the point P(0, 2, – 4) and the point Q(3, – 2, – 3). -

A: Given:P0,2,-4 and Q3,-2,-3

Q: Find the distance from the point (3, 1,0) to the line given by symmetric equations *** =-3, y= 1.

A: Given that: The point is: (3, -1, 0) and equation of line is:         x+42=z-3, y=1

Q: Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1) and…

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Q: Find the distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: Graph the image of parallelogram STUV after a reflection across the line y = x. 10 8 21 -10 -8 -1 -4…

A: Graph of the parallelogram is given, it is reflect about the line y=x

Q: Find the distance of the point (3,8,2) from the line =22= measured parallel to the plane 3x + 2y- 2z…

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Q: Which pointis two fifths of the way between point A and point B on the line segment AB shown on the…

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Q: Find the distance between the plances 3x + y - 4z = 2 and 3x + y – 4z = 24

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Q: Find Sax ds, where C is the line segment in the plane joining (0,0) and (3, 4).

A: I am attaching image so that you understand each and every step.

Q: Find the distance from the point (-2, 1, 4) to the plane y = -5

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

Q: Find x²z ds, where C is the line segment from (0,6,4) to (1,3,-2) C

A: ∫C y ds,  C: x=t2, y=t,  -2≤t≤3   dxdt = 2t,   dydt= 1∫Cy ds = ∫-23 t  (2t)2+1 dt=∫-23 t  4t2+1…

Q: Find the distance from the point (-4,3,-2) to the yz-plane.

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Q: how do i prove that the diagonals of a parallelogram bisect each other ? Then have to name…

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Q: What is the distance between the point (-2, 5, 3) and the z-axis?

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Q: Find the coordinates of the points that are 15 units away from the origin and have a y-coordinate…

A: Given y- coordinate = -12