5. Compute the flux of F = (x³, -x³ z², 3y²z) across the positively oriented surface z = 3-x²- y² capped by the plane z = 0 on the bottom. Make you sure to draw the surface.

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: What does 2x + y = 4 represent in the xy plane and what in the space?

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Q: The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector…

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Q: Draw v = [ 4/1 ] and w = [ -2/2 ] and v+w and v-w in a single xy plane.

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Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Determine the equation of a plane parallel to x-z plane which is tangent to the circle…

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Q: Find the parametric equations of the line tangent to the curve of intersection of the surfaces x² +…

A: The tangent to the intersection of the curves: f(x, y, z)=0, g(x, y, z)=0 is parallel to the vector:…

Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.

Q: Consider the equation of the surface S given by -3x - 2y³z4+ xy = -4 where a and Bare pair numbers,…

A: Use formula of equation of Tangent plane