he curve C is the intersection of the plane z + y = 2 and the cylinder x? + y? = 1. Assume a counter-clockwise traversal of the path Cif viewed from above the xy-plane poking down.

Q: and フドnd the eguafion f Plane hat Passes through PC1コーっる)mnel is Parallel te the Plane 3X++=7…

A:

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

A:

Q: Calculate fo(7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and radius…

A:

Q: Ewaluate by the planes x=0,y=0, t:0, for

A: Given - E is bounded by the planes x = 0, y = 0, z = 0 , y + z = 1 and x + z = 1 To find - Evaluate…

Q: 3-Find the equatium uf tue plone that is parllel and at (& units) Aujay From The plane (x-ay+t=3)

A: The equation of the given plane is  x-2y+z=3

Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

A:

Q: Sketch the plane curve and find its length over the given interval.

A: Given a function. We need to sketch the plane curve and find its length over the given interval [0 ,…

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

A:

Q: Prove that the parabola y = x^2 at the points where the line has an angle of inclination "o" the…

A: Curvature of  a graph y= f(x)  k=d2ydx21+dydx232

Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

A:

Q: Find a formula for the distance from the point P(x, y, z) to the yz-plane.

A:

Q: Let M C R³ be the set obtained by rotating the circle {(x, 0, z) E R³ : (x – 2)² +2² = 1} about the…

A: Solution is given below

Q: Let P be the plane that is tangent to the equation xyz + 260 = z' + 30x + 26y at the point (7,7,4)…

A: The tangent plane to the surface is a plane that only touch the surface at the point.

Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

A:

Q: Let r < R. Revolving a circle of radius r, (x – R)² + y² = r², around the y-axis gives a donut…

A:

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

A:

Q: .2 y = z, -2 < z < 2 %3D (x - 2)² + 4y2 = 4

A: (b)  The given equation is y=z2, -2≤z≤2. Observe that y-coordinate will always be positive and…

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

A:

Q: When is An angle in the xy-plane is said to be in standard position?

A: An angle is in standard position if its vertex is located at the origin and one ray is on the…

Q: (3) Consider the quadric surface SC R, having equation a2 + y? – 22 = 9. Find all lines through P =…

A: The quadratic equation is given by x2+y2-z2=9.  General equation of line is: x,y,z=a,b,c+tl,m,n…

Q: Find the eguatien of the tangett line and nemat plane to the cune; Y. cest Ces(zt)i + st sinCet) j +…

A: Given r=cost cos2ti+cost sin2tj+sintk

Q: The midpoint of AB is M(0, –4). If the coordinates of A are (2, –1), what are the coordinates of B?…

A: Given- The midpoint of ABis M0,-4. To Find- The coordinate of point B, if the coodinate of the point…

Q: 25. Determine the distance between the parallel line {y = 5-t, te R and the plane {y = 2-s -t, s,t E…

A:

Q: Find the equaition of a plane parallel throngh the a nor mal - zi+jtzk to poinl the plane Passing…

A:

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…

A: Find your answer below

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

A:

Q: Use Stoke 's Theorem to evaluate [ . dr, where v = y²i + xyj + xzk, and c is the bounding curve of…

A: We have to solve the given problem by using stokes theorem.

Q: Is the line x = 4+ 2t , y =-t , z = -4t – 1 parallel to the plane 3x + 2y + z = 7? %3D

A:

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

A:

Q: Find an equation for the projection of the curve on yz plane. O y + z? = 3 O y? + z? = 4 O y? + z? =…

A: For projection in yz plane equation must be in terms of y and z only. Here x=t y=3 cos t z=3 sin t

Q: Evaluate the line integral ſe ry²ds, where C is three quarters of the circle a² +y? = 1, oriented…

A: C is the three quarters of the circle x2+y2=1, oriented counterclockwise. The parametric equation of…

Q: Calculate fc((7x + 6y) i + (4 + 7y) j) · dr where C is the circular path with center (a, b) and…

A:

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

A:

Q: Find the equations of the tanget plane and normal line to the graph of In(z?) x - = 3y3 – Vx at the…

A: tangent plane and normal line

Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the midpoint of…

A: From the graph, it is clear that B is at (-1,2) and D is at (5,-2) Now, the midpoint formula gives…

Q: Show that the curve a(t) = (t, , ) lies in a plane and find the equation of this plane.

A: For all 't' , we have α'(t) = 1 , -1t2 ,-1 - 1t2α"(t) = 0 , 2t3 , 2t3 Now  α'(t) × α"(t) = 2t3 ,…

Q: Consider the level surface 2x2y + 9z = 3, the angle in degrees that the z-axis makes with the…

A: Given

Q: Evaluate F.dr, where F (x, y, z) = - yi + xj + z*k and C is the curve of intersection of the plane y…

A:

Q: Calculate fc((7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and…

A: The path is given as the circular with center (a, b). Now the integral is: I=∫C (7x+6y)i→ +…

Q: Suppose the plane So thet its Coordinates are a partile Pir moving in given by y=Fsinzt Plxy) where…

A:

Q: s the line perpendicular to the given plane?_ Construct plane UVW perpendicular to the given plane.

A:

Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

A:

Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: What is the equation of a plane whose r-intercept is a, y-intercept is b, and z-intercept is c?…

A: Solve for the equation

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n PS| d =…

A:

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x? +…

A:

Q: Let h VI and y: 8 For what value(s) of h, is y in the plane generated by vị and v2?

A:

Q: Describe your plan for proving the following.

A: Given that AM=MP and ∠AMP=90o. X can be thought of as a plane ground and AM is perpendicular (pole…