c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices (2,0,0), (0, 2, 0) and (0,0, 2) with anticlockwise direction when viewed from above.

Q: Find three different pairs of parametric equations for the line segmentthat starts at (0, 0) and…

A: Direction ratio is = (6-0, 6-0)= (6,6) That is equivalent to (1,1) , (2,2) and (3,3)

Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

A:

Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

A:

Q: 8. Find the parametric equations for the plane that passes through the points: P (2, -2, 3), Q (0,…

A:

Q: Find the distance between point A(-1,4,6) and the line of parametril equations x = 2-3t, y = -4+t, z…

A:

Q: Find a set of parametric equations of a line passing through the point (3,2,-1), parallel to the xz-…

A:

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

A:

Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

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: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows

Q: It can be shown that the parametric equations x = x1 + (x2 – x1)t, y = y1 +(y2 – yı)t, where 0 <t 1,…

A: Given: Parametric equation of line segment joining the points P1x1,y1 and P2x2,y2 is given as…