Use Stoke's Theorem to evaluate the line integral -4ydx +-3zdy+dz where C is the intersection of ralf-4 the xy -plane and hemisphere z = √1-x² - y² traversed counterclockwise viewed from the top-that is, from the positive z-axis toward the xy-plane.

Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

A:

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

A:

Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

A:

Q: 3. Find an equation of the plane parallel to the plane 4x -z- 3y -4 = 0 and passes through the point…

A:

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

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

A: Solution :-

Q: Determine a so that the line x-3/a=y+5/2=z+1/4 is parallel to the plane 2x+3y-5z=14.

A: To determine  so that the line  is parallel to the plane .

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

A:

Q: definition set and drawan the plane Find the

A: Using elementary properties of logarithmic function and square root function set is obtained then…

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

A:

Q: The domain is the entire xy-plane.

A: Domain -Domain constitutes only the values of x on which the function is defined.