10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut from the plane x+y+z=1 by the first octant, counter-clockwise when viewed from the above.

Q: 2. Find the distance between the line with parametric equations ï = 1 + 2t, y = −2+ 4t, z = 4 − 4t…

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Q: Use Green's theorem to evaluate O -x²ydx + x°dy, where C is the circle x? + y? = 4 with a…

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Q: LL" IIT F4x,y,.2) dz dy dx Sketch and shade representative traces parallel to or in the coordinate…

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Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

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Q: es v3x + z – 5 = 0 and 2x + 2/3z + 10 = 0. ond

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Q: Which of the following point is the farthest point on the sphere z? + y² + z² = 4 from the point…

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Q: Closest point is (If there is more than one point, enter a comma-separated list.)

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Q: FIND THE DIVERGENCE AND CURL OF U = i (x 2+ yz)+j Cy?+Zx) t K (z?+xy] %3D

A: Given :u=i x2+yz+jy2+zx+kz2+xy.We need to find the divergence and curl of u.

Q: Prove that a line intersects a paraboloid at' two points which may be real or imaginary.

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center of…

Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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Q: What is the value of f 4xy²dx + (4x²y + 2)dy when C is the part of the circle x² + y² = 1 from the…

A: Here, we will use the Green's theorem. According to Green's theorem: ∫CMdx+Ndy=∬(∂N∂x-∂M∂y)dxdy

Q: Find the point on the sphere X+y+=4 and the point on The sphere x+y ansi- 2 Selution:-

A: To find the point on the sphere which is farthest from the given  point (1,-1,1).