Find the point ( x, y) such that (1, 3) is the midpoint of the line segment connecting а. (х, у) and (-6, -4). b. (х, у) and (-3, 1) с. (х, у) and (2, -3) d. (х, у) and (3, 5)

Q: Verify that the two lines are parallel and find the distance between the lines. L1:   x = 2 − t,   y…

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Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line =…

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Q: Find the distance from the point (3,-1, 4) to the line z -2+3t, y = -2t, z = 1+ 4t.

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Q: calculate the distance between point(5,2) and the line, 2x+5y=10

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Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t ,y=-2t+1 ,z=t is

A: We are supposed to find the distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t…

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 equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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Q: Find the distance of the line 4x + 7y+ 5 = 0 from the point (1, 2) along the line 2x - y= 0.

A: Consider the provided question, (21) First find the intersection point of the two lines,

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

A: I am going to solve the given problem by using some simple calculus to get the required result.

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 the distance of the point (3, 2, –4) from the line r(t) = (1+ 3t, –1+ 2t, 3 – 3t).

A: for finding distance of the point3,2,-4 from line rt=1+3t, -1+2t, 3-3t we assume a point1+3t, -1+2t,…

Q: The midpoint of a line segment whose endpoints are (x1, y1) and (x2, y2) is (______ ,________ ).

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Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

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Q: Find | x²z ds, where C is the line segment C from (0,-3,2) to (-3,-2,8)

A: Given C is the line segment from (0,-3,2) to (-3,-2,8) Now write the parametric equation for C…

Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

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: Find distance from the point (0, 1, 3) to the line = 2t, y = 6–2t, z = 3+t

A: (0,1,3)    L=x=2t, y=6-2t, z=3+t

Q: The distance between the point (9, 8, 3) and the plane x + y−2z = 5 is _____.

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Q: write down the equation of the pair of straight lines joining the origin to the points of…

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Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and…

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and…

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: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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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 distance between the point (-1, 5, 3) and the line given by x = 5 + t, y = 1 - 2t, and z =…

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Q: Find the distance from the point (3,-1, 4) to the line a = 4 – t, y = 3 + 2t, z = -5+ 3t.

A: Given: point 3,-1,4 and equation of line x=4-t, y=3+2t, z=-5+3t Formula: The distance between point…

Q: Find the distance from the point (-6,-2,0) to the line a(t) = ( – 1, – 2, – 5)t + (3, – 6, 6)

A: We  use the definitions

Q: find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

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Q: Find the midpoint of the line segment from P1=(-5,5) top2=(3,1) . Plot the points p1andp2 and their…

A: given,     a line segment from p1=-5,5 and p2=3,1

Q: find the distance between the Linel L) through A(I,0,-1), B (-1,)andthe Line (L2) through C…

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Q: Find the distance of the point (4, 2, -4) from the line r(t) = (1+2t, 1+ 2t, 7 - 3t).

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Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: What is the midpoint of line segment XY with coordinates X (-4, 10) and Y (8,6)? (-6, 2) (3, 7) (-7,…

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Q: Find the equation of line L through the point (5, 7/2, 5) intersecting at right angle the line M…

A: Given that, the line L is passing through the point 5,72,5 intersecting at right angle the line M…

Q: Find an equation of the plane through (4, 5, 7) that is - 2 = 5t, y +3 = 10t, z = -5t. perpendicular…

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Q: Find the distance between the two straight lines and x=1+1, y=2, z= −1+2+ x=2-t, y=3t4t, z=2t at the…

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Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

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Q: Find the distance between points P1(0, 0, 0) and P2(-6,-2,5).

A: Distance = x2-x1+Y2-Y1+z2-z1

Q: Find distance between two lines x = 1 + t, y = 1 + 6t, z = 2t and x = 1 + 2s, y = 5 + 15s, z = -2 +…

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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: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: Calculate the direction of P₁P2 and the midpoint of line segment P1P2- P 1(3, 4, 6) and P 2(6, 0, 1)…

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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: find distance between point A(2,-4) perpendicular on the line L: 3x- 4y=17 6.5 O 7.22 O 4.79 O 6.22…

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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: 5- Find the distance from the point to the line. a. (0,0, 12); x = 4t, y = -2t, z = 2t b. (0, 0, 0);…

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Q: standard form of the line with center (5,1) and tangent to the line 7x+2y=17

A: Given Data: Center: (x1, y1) = (5, 1) Tangent: 7x+2y=17   The general equation of tangent is,…

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: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

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

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