Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

Q: Find the distance between the following skew lines -y+14, z= X-1 y =z+3 2 2

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Q: ind the point P on the line y = 5x that is closest to the point (78,0). What is the least distance…

A: This question is related to straight line. we will solve it using the condition of shortest distance…

Q: Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.

A: Consider the provided information, Find the point P. The normal vector to the plane is 1,1,1. And…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the distance between the skew lines: x = 9+ 6t, y = 5 + 6t, z = 7 – 6t y = 7, x = 7 – t, z = 6…

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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Q: Find the distance between the skew lines defined by L1: ri(t) = L2:r5 (s) =

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Q: Find the distance from the point S(1, 1, 5) to the line L: x = 1 + t, y = 3 – t, z = 2t.

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Q: Find the distance between the following skew lines -y+48, ,z=0

A: The given equation of skew lines- x2=y+48,z=0x-12=y2=z+3 Above equations can also be written as-…

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

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Q: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. O (5)^0.5 O 7 O 2(3)^0.5 O…

A: Given: Equation of line is: X = 1+ t Y = 3 - t Z = 2t To find: distance from the point (1, 1, 5) to…

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Find the distance between the skew lines: x = 8+6t, y = 5+ 9t, z = 7 – 5t y = 9, I = 6 – t, z = 2+…

A: Given, x=8+6t, y=5+9t, z=7-5tx=6-t, y=9, z=2+4t To find: Distance between the two given skew lines

Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Find the distance between the given skew lines: x = 4+9t, y = 5+ 3t, z = 7- 6t x= 8 – t, y = 9, z =…

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Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

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

A: Given query is to find the the distance between point and the line

Q: The distance between the two lines x = 1+ t,y = -2+ 3t, z = 4 – tand x = 2s, y = s, z = s is

A: Please see the explanation below

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

Q: Find the line through (1,-1,1)and normal to the line  3x=2y=z , and parallel to the plance  x+y-z=0…

A: Equation of the line: The equation of a line passing through the point (x0, y0, z0) is given by (x,…

Q: Find the distance between the skew lines: x = 5 + 8t, y = 1+ 6t, х— 2 — t, z = 4 – 9t z = 4+ 8t y =…

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Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1…

A: Given: The planes: 2x+y-z=1 and x-y+z=2.

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

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Q: Find the length of the curve. y = In(secx), 0Sx</4

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Q: Find the distance between the skew lines: I = 9+9t, y = 2+5t, z = 3-7t x=6-t, y = 9, z = 6+6t NOTE:…

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: Find the distance between the skew lines defined by L1:(t) = L2: r2(s) =

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Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: Find the distance between the skew lines: y = 1+3t, y = 9, x = 3 + 8t, z = 4 – 9t x = 5 – t, z = 4+…

A: Given equation of line L1: 3+8t   , y=1+3t   , z=4-9t L2:   x=5-t  , y=9   , z=4+8t

Q: Find the distance between the skew lines: x = 5+ 6t, y = 2+ 3t, z = 8 – 3t z = 1+ 2t x = 9 – t, y =…

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Q: O whion of the line: y--2x+8 Poliowing line5 ave perpendicular to this. B. ut

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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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 shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.