3. a) Compute: f (Rez-32) dz where I is a directed line segment from z=0 to z=i. b) Let C be the circle |z| = 4 traversed once in the positive sense (counter clockwise). Compute: dz 2² (2-5)

Q: 8. Find the point (x. y) such that (1, 3) is the midpoint of the line segment connecting a. (x, y)…

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Q: What are the directing cosines of the line whose symmetric is (x + 2)/ - 1= (y-3)/ 2 = (z + 4)/ 6

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Q: Q5) Find the coefficients a, b, c and d such that the curve defined by; y = ax³ + bx² + cx + d,…

A: Given: The curve y=ax3+bx2+cx+d passes through the points 0, 10, 1, 7, 3, -11, 4, -14. To find: The…

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: Which of the following functions satisfies the partial differential equation Tuz+yuy = 0. O e=²+3² O…

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Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

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Q: Let C be the line segment connecting the points P(−2,1,−4) and Q(5,−4,3). Evaluate ∫C(2x+4z)dy…

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Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

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Q: 2. Sketch the line = (-4,-4) + t(6,8).

A: To sketch the line r=(-4,-4)+t(6,8)

Q: Give the coordinates of X-intercept for the line Y = 2(x – 1) + 7.

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Q: Q6) 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: Please

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Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: 7. Find the distance from the point A to the line through the points B and C where A, B, and C have…

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Q: What is the distance between the points M(-3,1) and N(7,-3)?

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Q: i 6i + 2j+ 2k + 2(i- 2j+2k) Find the shortest distance between lines -4i -i + 4(3i - 2)- 2k) and

A: The given lines are as follows- r→=6i^+2j^+λi^-2j^+2k^          ........(1)r→=-4i^-k^+μ3i^-2j^-2k^…

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

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…