Part (a) Evaluate 100e dz, where C'is the polygonal path consisting of the line segments from z = 0to z = 2and from z = 2to z = 1+ ri

Q: A Curve a with aca) = (2,4,4), 2e2) = (0 ,2 54). %3D %3D Find Kea), B)

A: We will find out the required value for given curve.

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A: To find the distance from the point to the line.

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Q: Evaluate A = F. dr where F(x, y) = (6x – 2y)i+x²j for each of the following curves. a) C is the line…

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Q: Evaluate (x + y)ds where C is the straight-line segment x = 4t, y = (12-4t), z = 0 from (0,12,0) to…

A: Let  where C is straight line segment  from .We know thatwhere

Q: find the sLope Of a tangent line hCx) = x +44 iz

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Q: 6a. Find . F dr, where F(x, y) = , and C consists of the circle x' + y = 4 from (2,0) to (v2, v2)…

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Q: Consider point P(4, 2) and line l with equation −3x+4y=6 .

A: Substitute x=4 and y=2 into the given equation. -12+8=-4

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A: As per guidelines i can only solve the first question in multiple questions.Finding the equation of…

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

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Q: Suppose that we start at the origin in the xy-plane and take n unit steps (i.e., each step is of…

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Q: Let y = d -7 = 7 and u = -7 -2 Compute the distance d from y to the line through u and the origin.…

A: Introduction: Let l be the path connecting the origin to u. We can compute the projection of y onto…

Q: c. Evaluate f 3x ds, where C consists of arc C₁ of parabola y = x² from (0,0) to (2,4), followed by…

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Q: br II) passing through P=(2,-1) and is perpendiculed to the line √x=2-t y=3 In normal form.

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Q: Find the angle between the following pair of lines: £ =2? =5] +k + 2(3 + 23 + 6k) and = 7i — 6k +…

A: A vector in the three dimensional space is represented by v=ai∧+bj∧+ck∧, where a, b and c are the…

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: Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2,…

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

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