State Green's Theorem. Use it to calculate . ((13x – 5y)i + (13x + 5y)j) dr where C is the circular path with center (5, 13) and radius 11 oriented counterclockwise.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

A:

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Find the standard equation of the sphere with center C and rad C(1, v2, -5); r= 3

A:

Q: Find the equation of the perpendicular bisector of side of the triangle having vertices…

A: Slope of a line passing through two points x1,y1,x2,y2 is given by Y2-x1x2-x1 Midpoint of two points…

Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use Green's Theorem to calculate ( - sen(a))da + (2a + 3)dy, where C is the triangle with vertices…

A:

Q: XZWY is a rhombus with diagonals XW and ZY intersecting at point M. Given YMX = 3p + 6, solve for…

A: diagonals of rhombus makes right angle at ntersection point

Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

A:

Q: Identify the quadric surface satisfying each of the given equations and then make a rough sketch to…

A: identify the quadric surface satsifying each of the given equations and make rough sketch to show…

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: In the parallelepiped below, we know that (ū A ü). W = 6. Additionally, ū = (1, 1, 0) and i= (0, 1,…

A: Given that:                        (u∧v).w=6u=(1,1,0)v=(0,1,1)

Q: Which of the following points is on the xy and yz planes, but is not on the xz plane? a) (2, 0, 0)…

A: We can represent 3D coordinate system.

Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

A: Part(a): Given, The point is a,b,c  And, the plane is, Ax+By+cZ+D=0

Q: • Which of the following conics is a trace on one of the coordinate planes of the surface whose…

A:

Q: Let a point a = (2, 4, 5). %3D a) Find the distance from this point to the xy-plane.

A: Consider the point

Q: Show that the curve a(t) = (t,4,²) lies in a plane and find the equation of this plane.

A: Solution:- αt=t,1+tt,1-t2t t,1t+1,1t-t=x,y,z It is clear that, t-1t-1+1t-t=x-y+z x-y+z=-1

Q: Name two planes that intersect in FG.

A: We have to name the plane which intersects in FG,

Q: Which of the following points is on the xz plane? a) (1, -3, 0) b) (0, 4, 0) c) (0, 3, -2) O d) (2,…

A:

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below with…

A:

Q: -dA where R is the triangle of vertices (0,0), (1.0) and (0, 1). answer: 0

A:

Q: nat is

A:

Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: Evaluate fc(-5zi + 5yj + 6xk) · dr, where C is a circle of radius 4, parallel to the xz-plane and…

A:

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A: Given 11, 35, 06, p=23 let a=11, b=35, c=06, p=23 Now we write the points in augmented matrix form…

Q: a. A trapezoid has been transformed on the coordinate plane as shown. Trapezoíd A Trapezoid B

A: Given that:

Q: Which of the following planes contains the z-axis?(a) z = 1 (b) x + y = 1 (c) x + y = 0

A: In 3 dimensions, the rectangular coordinate system has 3 perpendicular axes, x, y, and z. Any point…

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

A:

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A:

Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

A:

Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

A:

Q: 2. Do the two planes intersect? If they do, where do they intersect? TT 2x - y + z = 1 = 0 3 TT 4 x…

A: Equation of the line perpendicular to the given plane be n1 & n2 . Now here n1≠ k n2  , where k…

Q: Find the shortest distance between the point (1,0,-2) and the plane z+2y+z 4. Put your answer in…

A:

Q: Calculate y°dz – yz²dy – sen(2)dz, where C'is the path connecting the point A(-2, 2, 4) to the point…

A: We will calculate the integral ∫Cy2dx-yz2dy-sinzdzwhere path starts from point A-2,2,4 to the point…

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

A:

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

A:

Q: An equation of a plane P passes through the point (0,0,3) and perpendicular to the line L:x =1– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: Find an equation for the plane that passes through the point (1, 2, 3) parallel to u = 2i + 3j + k…

A: Given:u = 2i + 3j + k and v = i - j + 2kFirst find cross product

Q: Di+Oj

A:

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

Q: Let u = 2 and v = | 0 , and let P = span{u, v}. Find an equation for the plane P.

A: Given: Let xyz be a point in Span {u, v} so there are t, r∈ℝ such that xyz=tu+rv. So,…

Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any nonzero numbers a, b, and c. Which planes…

A: Given equation of plan is xa+yb+zc=1   ...(1) Where a, b, c≠0

Q: ind an equation for the plane that passes through the point A(1,2,3)parallel to u = 2i + 3 j + k nd…

A: