13. Evaluate (2x + y + 3z) ds, where C is the straight line from (0, 1, 1) to (1,0, 1).

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

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Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 20. Evaluate l Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: 2. Evaluate S. 3x – 6y ds for C is the line segment from (6,0) to (6,6).

A: Solution

Q: Evaluate (x+ y)ds where C is the straight-line segment x = t, y= (4- t), z=0 from (0,4,0) to…

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: Evaluate the line integral 4ydx + 2xdy where C is the straight line path from (4, 2) to (8, 4).…

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Q: 4. Evaluate fo (3x + y)dx + (2y – x)dy along the straight line joining (0, 1) to (2, 5).

A: We need to find the line integral ∫(0,1)(2,5)3x+ydx+2y-xdy .  We first parametrize the line segment…

Q: 44. Select the pair of lines that are parallel. O 5x – 2y = -1 y = 4x – 1 4x – 6y = 6 2x – 3y = -6 -…

A: two parallel lines is of the form  ax+by=c and ax+by=d where a,b,c,d are constants

Q: 2. Evaluate (x² + iy) dz, where C is the straight line from z = 1 to z = i.

A: to find  ∫Cx2+iy3dz,  where C is the straight line from z=1 to z=i proof using giving condition we…

Q: Evaluate (x+y)ds where C is the straight-line segment x = 2t, y = (8 – 2t), z = 0 from (0,8 C…

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Q: (1) What is the relationship between lines 11 and 12? where L:x = 2, y = 1+2t, z = 1+t L2:x = 4 -t,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate ∫C x ds, where C is the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).

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Q: 20. Evaluate J Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

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Q: 3. The line L is parallel to the line x t, y 2t, z =3 and passing through the origin.

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Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

Q: 16) Identify the hortizontal line. A) y=x C) y=-5 E) x= 4 B) x -y 1 D) x+y 0

A: Line Parallel to x axis

Q: 21. Reflect in the y-axis. 5- 4- 2+ х -2 -3+ -4 T'(2, 2), V'(4, 1), W'(5, 4), X'(0, 4) b. T(-2, -2),…

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Q: 1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

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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 distance from the point S= (1, 2, 1) to the line x = 2-t, y=-1+2t, and z=2+ 2t.

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Q: 51. Show that the shortest distance from the point (x1, yı) to the straight line Ax + By + C=0 is Ax…

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Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: The area bounded by the curve y=4x y=4x  and the lines x=6x=6 ,x=10x=10 and x−axisx−axis is: Choose…

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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: fc z2 dx+ x2 dy +y2 dz, C is the line segment from (1,0,0) to  (4,1,2)

A: Given, r(t)=z2dx+x2dy+y2dz We have the line segment from (1,0,0) to (4,1,2) We parametrize the given…

Q: Evaluate S(-x+y+z) dx + (x+y-3) dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: 1. (x² +y² +z?) ds , where Cis straight line from (1,2,3) to (4,1,4).

A:

Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: 1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) :…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: 2 1ど y+1 w that line

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Q: * Let LIEX-54+10=D0 L2=4X+y-1-O be two lines. 1 Show that the lines L and Lz are not parallel.

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Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

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: Scalar line integrals Evaluate the following line integral along the curve C.

A: Given:  where, C is the line segment from (-1,0) to (0,1) followed by the line segment from (0,1)…

Q: 1. Show that the lines 2x + 3y = 1 and 6x - 4y - 1 0 are perpendicular.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

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Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

A:

Q: Evaluate | (x + iy' ) dz, where C is the straight line from z =1 to z=i.

A: given, C is the straight line from z=1 to z=i claim- evaluate the integral ∫Cx2+iy3 dz

Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

A:

Q: Find Sc((x² + 3y)i + 3y³j) · dr' where C consists of the three line segments from (2, 0, 0) to (2,…

A: Given ∫x2+3yi→+3y3j→.dr→ where C consists of the three segments from (2,0,0) to (2,2,0) to (0,2,0)…

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

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Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: X. xy ds where C is the straight line from (2,3) to (4,0).

A: Given: The curve C is the straight line from 2,3 to 4,0, To find: The value of ∫Cxy2ds.

Q: If u=2x+y and v=x-2y then the st ream line is y2 x2 2ху+ 2 صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

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.