| xyz2 ds, C is the line segment from (-1, 5, 0) to (1, 6, 5)

Q: Find the distance between the point (5, 1) and the line y = 3x + 1. O 3V10 O 7/10 O 9/10 O 5V10

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Q: Find k so that the line through (4, -1) and (k, 2) is a. parallel to 2x + 3y = 6, b. perpendicular…

A: The line passes through the points (4, -1) and (k, 2). Then the slope (m) of this line is: m = [2 -…

Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

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Q: What are the equation of line passing through (-1,3) that is tangent to the curve x^2 + 4y^2 – 4x –…

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Q: 6. Parallel to the line Y = = -}(x – 100) – 99, 3 4 passing through (1, 3)

A: Given query is to find the equation of the line passing through (1,3) and parallel to the line…

Q: -) that passes through (-1,3) that is parallel to 2x – 5y = 1

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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 image of the line x = 1 under (a) flz) = z²

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Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13=0 in which the tangent line…

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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: 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: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

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Q: Find the shortest distance between the skewed lines. l1: = 1+ 2t, y = -1+t, z = 2+ 4t and l2: x= -2+…

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Q: Two straight lines 3x – 2 y + 5 = 0 and 6x – 4y + 10 = 0 intersect at the origin. are coincident.…

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Q: Find K so that the line through( 1, 5 )and( K, 8) is a) parallel to 4y -3X =7 and b) perpendicular…

A: compute the equation of a line joining (1,5) and (k,8) by using below formula.

Q: 3- The line jaining the origin and Point_of intersection of the linesr(X=l+2t_ ys-3+4Ł,2=t) aul (x-…

A: Given that: Lines are: L1: (x=1+2t, y=-3+4t, z=t) and L2: (x=-2+3t, y=-5+3t, z=-12+34t)

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

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Q: Find an equation of the line through the point (1, 2) that is perpendicular to th = --x +3 Select…

A: The given question is solved below.

Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: d the eqation of the line that passes through A(1,2,1) and intersects the line x+1 у-2 z+1 %3D at…

A: Topic:- geometry

Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: Evaluate ryz ds, where C is the line segment from (3, 0, 1) to (0, 2, 5).

A: Given function is ∫Cxyz ds Given points are r1=3,0,1 and r2=0,2,5 We can write the given points in…

Q: Show that -ydx+xdy) = x₁y₂-₂₁ where C is the line segment joining (x,y) and (x₂,₂).

A: We have to prove ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1,y1 and x2,y2 Now…

Q: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 .B O 16/77 .c O 56 3…

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Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

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Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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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 the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

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Q: Two straight lines 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 intersect at the origin. are coincident. are…

A: This question is based on straight line intersection.

Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

Q: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

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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: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 77.B 16/77 .c O 56 3…

A: The line segment is from 4,1,5 to 0,6,-1 . Hence, this line is parallel to the vector, 4,1,5-0,6,-1…

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: So Find x²z ds, where C' is the line segment from C (0,-5,4) to (-6,-4,3)

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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: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: What is the image of (4,-1)(4,−1) after a reflection over the line y=xy=x?

A: Reflection over y=x means:  (x,y)→(y,x)  We need to find reflection of (4,-1) over y=x line .

Q: Find the equation of line passing through (5, 8) and perpendicular to y - axis. Oy = 5 Oy= 3 Ov=0 Oy…

A: The general equation of the straight line is: y=mx+c Now, the slope of the y-axis is infinity. So,…

Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

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Q: Evaluate (x + y) ds, where Cl is the line segment from (-2, 1, –5) to (-1, –1, –2).|

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

A: we have to evaluate

Q: A line that is normal to the curve x^2+3xy-4y^2=0 at (6,6) intersects the curve at what other point?

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Q: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

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Q: Show that the product of the perpendicular distances from the origin to the pair of straight lines…

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