Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

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

A:

Q: Find the work done by the force F = y2i + x3j, where force is measured in newtons, in moving an…

A: To determine the work done by the force.

Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

Q: Find AB. In Exercise 3, CB is tangent to OA. 3. 1. С 2. C 5V3 30° A B A В 6 С

A: Given ABC is a right angled triangle.we have…

Q: Sketch the plane curve r(t) = t2i − 4tj and find its length over the given interval [0, 5] .

A:

Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

A:

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

A:

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

A:

Q: Evaluate //. dV, where E x2 + y² + lines between the spheres x + y + z? and x + y? + z2 = 25 in the…

A: Consider the provided question, Evaluate ∫∫∫E1x2+y2+z2dVwhere, E lines between the sphere x2+y2+z2=1…

Q: Consider the curve C parametrized byx = (t^2+1)/(t^2-1) and y = (2t)/(t^2-1) for all t in (−∞, −1 )…

A: Given:

Q: Sketch the plane curve r(t) = t3i + t2j and find its length over the given interval [0, 1] .

A:

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

A:

Q: Evaluate e dz where C is the line segment from 0 to 2+2i, parametrized by z(t) = t + it?.

A:

Q: (a) Let r = where C is the unit circle oriented counterclockwise, and Vr2 + y?. Calculate fF Tds…

A:

Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

A:

Q: 12. Evaluate 3x ds where C is the parabolic are along y from P(0,0) to Q(2, 2).

A:

Q: ut (X, Tof) be the cofinita to p. Jet A = {1,3]. etス=R B= Co1) %3D Fnd Ā ļ B.

A: Here given that X=R  Let A={1,3} and B=(0,1)

Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: Sketch the plane curve. r(t) = 4ti - tj, [0, 4] y y 4 4 2 10 15 10 15 o-4 o-4 y y 4 X 5 10 15 10 15…

A:

Q: For the following position vector valued function  r(t) = (3t^2, -2t^2, 4)  find the arc length…

A: Given:  r→t=3t2-2t2,4To find:-  Arc length from   t=0  to t=5

Q: Q solve the followngdifferentral equations using laplace transhorm. with ylu)=6, y(o)= 13 1-

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: H.W: find the angle between the planes x + y = 1 and 2x + y- 2z = 2

A:

Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

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

A:

Q: 1 Evaluate dV, where E lines between the spheres a? + y? + z² = 25 and %3D x² + y? + z2 49 in the…

A:

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

A:

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

A:

Q: A solld is obtained by rotating the shaded reglon about the specifled line. about the x-axis y y = V…

A: The given surface are y=x and y=20-x. The area between the two surfaces is obtained by ∬dx dy.

Q: For the line through (, 4) and (- = (Use symbolic notation and fractions where needed.) -) find the…

A:

Q: find the distance d(u, v) between u and v in the given exercise.

A:

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

A:

Q: Scetch the curve y and calculate , f(2) dz: a) 7(t) := t+i cos(t), te [0, 27], f(z) = R(2); b) y(t)…

A:

Q: Let r(t) = (sin 2t ,3t, cos 2t), -n SIST, a) Is speed always constant? b) Show that the velocity and…

A:

Q: IF=(x+y)i+(y– )j+z?k over the curve r(t) = (t²,t²,t*), 0sts1

A:

Q: W is the midpoint of VX and Z is the midpoint of VY. If XY = t +41 and WZ = t, what is WZ? %3D W WZ…

A:

Q: For the position vector R(1) = e'i+e²ª j, the velocity at t=ln3 is:

A: Consider the given position vector: R→t=eti+29e2tj Find Velocity vector: Differentiate w.r.t "t",…

Q: Consider z = Ax + By + D be the tangent plane to f (x, y) = 5x² + 10y³ + 6xy + 8x + 7y at (-0, 4).…

A:

Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

Q: Given the function f (x,y) = e* + sin(2y). the point Po = (0,0) and a unit vector = (cos 0, sin 0).…

A: Here we have to find directional derivative of f at P0 in the direction of v. Formula for…

Q: The surface differential, dS, corresponds to: A) u/2u² + IdA в) и? (4u? + 1) dA C) uv4u² +1dA D)…

A:

Q: Q, Solve he differnktial equntion by Laplace troms form. ý-y =t, yW=1, ý(0) =1

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

A:

Q: Evaluate c (xy + y + z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0st<1.

A:

Q: Sketch the plane curve r(t) = t2i + 2tk, and find its length over the given interval [0, 3]

A: We have, r(t)=t2i+2tk  we have to determine the length of the curve over the interval [0,3]

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

A:

Q: Use Gauss's D.T. to evaluate SSA.ds where Ã=x'i+y°§+7f qud S is the , surdace of the sphere x+j+z²=…

A:

Q: Given r→(t)=⟨cos⁡2t,−sin2t,4t⟩, find the unit tangent vector

A:

Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

A: