Evaluate .n dS and .ndS if F = (x + 2y)i– 3zj +xk, , and S is the surface of 2x + y + 2z = 6 bounded by x =0, x = 1, y =0 and y = 2.

Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

A:

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: 3. Sketch the parallelogram spanned by (2, 1, 0) and (-3, 1, 0) in the xy plane and find its area.

A:

Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Apply Gauss's theorem to evaluate. A

A:

Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

A:

Q: Draw the standard yz− and xz− traces of the quadratic surface x^2 + y^2 − 2x − z + 1 = 0

A: