Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).

Q: 7. State the linearization, L(r, y), of f(x, y) for the point (4, 3). f(x, y) = x3/² y Next, use the…

A: Given that  f(x,y)=x^(3/2)y  To find the linearization of f(x,y)

Q: 11. Find F. dr where F(x, y) = (3y, -2x) and C is the path starting at (0,0) to (4,0) to (4,4) back…

A:

Q: Find the following statement is true? ' W[y1,y2] = 0 implies y1 and y2 are linearly dependent'

A:

Q: What is the composition of the translations (T T) (x, y) as one translation? and q = (T T)(x, y) =…

A:

Q: Let C be the oriented line segment starting at (0,0) and ending at (1,2). Calculate Fn ds, where…

A: Given: C is the line segment whose initial and ending point is 0,0 and 1,2 respectively.…

Q: 1 3 - -- () ---- () 5 V2 = 10 3 12 4. Let VI: a) For what values of his v3 in Span {V₁, V2} ? b) For…

A: The given vectors,.The objective is to find the values of  for which the vector  is in the  and  are…

Q: Let C C R³ be the directed line segment from (1, 1, 1) to (3, 2,0). Evaluate

A:

Q: Compute fe F·dr

A: Green's theorem states that  ∮C(Ldx+Mdy)=∬D∂M∂x-∂L∂ydxdy…

Q: Let C be the oriented line segment starting at (0,0) and ending at (1,2). Calculate Sa F .n ds,…

A: To calculate the below line integral. ∫CF⋅nds Here Fx,y=y,−x C be the oriented line segment…

Q: 11. Let F(x, y, z) = = (), and let P represent the path that follows the from (1, 0, 1) to (0, 1,0),…

A:

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: 4. Define the function T: R² → R as 1 T(v) = Av = |-2 4 V2 %3D -2 a. Find T(2, 4). b. Find the…

A: We need to find pre image.

Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

Q: 6a. Find . F dr, where F(x, y) = , and C consists of the circle x' + y = 4 from (2,0) to (v2, v2)…

A:

Q: Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to…

A:

Q: Evaluate S2xyzdx + x²zdy + x²ydz over the path c(t) = (t², sin(πt/4), et²-2t) for 0 ≤ t ≤ 2. help…

A:

Q: 5) Consider the vector function r = (9- 2t, 4+2t, √2t²) a. Find the length of the path on 0 ≤ t ≤1.…

A:

Q: If W is a standard Brownian motion, compute P(W(1) + 2W(2) > 1).

A: W is a standard brownian motion. A standard Brownian motion at different times follows a normal…

Q: 14. Calculate | (y? – z)dx + (2ry)dy+(2z-x)dz where C is the path along (t2 + 4t + 2, V4+ 5t, t –…

A:

Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: . Find k so that the following pairs are orthogonal: = (3, k, 7, –5) in R“. 2. f(t) = t + k and g(t)…

A: Two non-zero vectors are said to be orthogonal when their dot product is zero.

Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0, 0,0) to (1, 4, 4).

A:

Q: c ls tE line cregmentfoom (3,4,0) to | (1,4,2) computef (zty?)ds&dp

A: The curve C is the line segment from 3,4,0 to 1,4,2. The parametric equation of this curve is given…

Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

A:

Q: Let c denote an arbitrary constant. Determine the orthogonal trajectory of x+xIn(y) =c that passes…

A:

Q: Show that r|(1) and r2(1) define the same line, where rị(t) = (3, –1, 4) + t (8, 12, –6) r2(1) =…

A: Two lines have the same direction if their direction vectors v1→ and v2→ are directly proportional.…

Q: Let F(r, y, z) = (y+ z²) i+ (x² – y)j+(z² – x) k, and let C be the piecewise-linear path from (1,…

A: answer  D correct option

Q: F.dr for F(x, y, z)=(x²)i+(x²y)j-(y²z)k where C is given by the vector 1. Evaluate Fa C function…

A: