Let u = f(r, s),r = x + at, s = y + bt, where x, y,t are independent variables and, a and b are constants. Show that du du +b. dy du = a

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: PDE ut- 3leuxx 0LXLI も>6 B.C.: : ulo,t) = ULyt)=D0

A: In this question, we solve the wave equation by using the separation of variable,s and using given…

Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

A:

Q: Suppose that u · (vxw) = 47. Find u. (wxv). u. (wxv) = i

A: Given: u·v×w=47To find:u·w×v

Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

Q: дz If z = f (x, y), find and for the following equation ду дz дх

A:

Q: Show that U(−f, p) = −L(f, p) and L(−f, p) = −U(f,p)

A:

Q: -351 ye dc -3 tanx dx t. tan x (e-casx) dy =0

A:

Q: Calculate fz(3, 6, 9), where f(x, y, z) = xyz. fz(3, 6, 9) =

A:

Q: Find ∂w/∂v, if w = 3x4-5y3+z5-10, x = 3u-4v, y=5u+2v, z = u+8v. Write in terms of the two…

A: Chain rule of derivatives

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

Q: uppose ū = (1, −3,−1) and v = (1, -5, -5). Then:

A:

Q: what values ofh Is V3 ea4 (9) lineasly dlependnt? values of h is {v, VzNs} Justiky answer tined - 2…

A:

Q: Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin (t). Find af af and (write your…

A:

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: Siny dx t sin Zydy + x dy

A: To solve: sin⁡ydx+sin2⁡ydy+xdy=0…

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)