If v = 3i - 6j and w = i + j, find (v . w)w.

Q: V=xincペッゴ)- y bii 24 Gan prove メT5 I V, = V +2X

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Q: Find əw/ar and aw/as when r = n and s = 0 if w = sin(2x – y), x = r + sin s, y = rs.

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Q: If w = f(x, y) and x = r cos θ, y = r sin θ, find formulas for ∂w/∂r, ∂w/∂θ, and ∂2w/∂r2.

A: Answer(1): Given that, w = f(x, y)  and  x = r cos θ, y = r sin θ Now, to find formulas for ∂w∂r,…

Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: If v=−5i+j and w =4i+j, find |v + w|.

A: Given,           v=−5i+j and w =4i+jTo find: v+w

Q: Let v = 3i + 6j and w = 3i + 4j. Find a number c so that w cv is perpendicular to v.

A: Two vector are given  v= 3i+6j and w= 3i +4j Now new vector w-cv is perpendicular to v then value of…

Q: Find (au / ay) at the point (u,v) = (√6, − 1), if x = u² + v² and y= uv. ди (2) (Simplify your…

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Q: aw and ar Q2) Find if as w = 2x + 4y - z, r+s X =r tan (s), y= sin (r - s), z=e**s.

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Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Given v=3i+j+3k, w=i-k

Q: If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

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Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: Use the substitutions : = ye S =X Q.3 to solve the du + y Əx PDE : %3D х, и(1, у) — сos y.

A: Using the substitutions we will solve for the PDE given as follows: ∂u∂x+y∂u∂y=x ∂u∂x+y∂u∂y=x…

Q: From v = [ 2/1 ] and w = [ 1/2 ], find the components of 3v +w and cv + dw.

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Q: If ds dt Vst , and t = 0 and s = %3D 1, find s when t = 9. A. 81 В. 100 С. 121 D. 144

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Q: Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

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Q: 16w Given that, w =1- 2i and z = w – Calculate z.

A: w=1-2i and z=w-16 ww2

Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: If a particle is moving with v(x)=1.5(x^1/2) and s(9)=33, what is the position of the particle? As a…

A: Let v(x) denote the velocity of the particle and s(x) denote the position of the particle.Obtain the…

Q: Find the indicated quantity, assuming u = 7i + j, v = i - 3j, and w = 3i + 5j. (u + v) · (u – v)

A: Givenu=7i+jv=i-3ju+v=7i+j+i-3j=8i-2ju-v=7i+j-(i-3j)=7i+j-i+3j=6i+4j

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: Find r(t) and v(t) if a(t) = 8 cos(t)k, v(0) = 4i + 6j, and r(0) = 7i. v(t) r(t) %3D

A: We have given: at=8cost kv0=4i+6jr0=7i We know that at=dvtdt So, we can write this as: dvt=at…

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: find the value(s) of a making v⃗ =7ai⃗ −3j⃗ parallel to w⃗ =a2i⃗ +6j

A: We have to find the values of a

Q: Given y = sin u and u = 3x + 1, find %3D %3D 9.

A: We have to solve the derivative

Q: Be w = (u2 + v2)3/2, where u = e-t sin(θ), v = e-t cos(θ), calculate: ∂w/∂t and ∂w/∂θ

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Q: Given u(x,t)=(1/t)e^(x^2\4t), compute: uxx

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Q: Convert the ! √ √4-1² 2 0 following to rectangular 32 r³z² sino cos o dz dv do dz dx dy

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: if z sin とこ3r'+25 , Y=4イ-ス3 Z = 2r-35* W= Z Sin %3D * find aw,w ar me' me as

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Q: Find the indicated quantity, assuming u = 6i + j, v = i - 3j, and w = 3i + 7j. (u + v) · (u – v)

A: We know,  i·i=1 ; i·j=0 ; i·k=0j.i=0 ; j·j=1 ; j·k=0k.i=0 ; k·j=0 ; k·k=1

Q: dw -is equal to: dv If w = 5u, then 5w5 v(1 – 20u In v) 5w v(1 – 20w5 In v)

A: Given, w= v5w⁴ To find, dw/dv

Q: Use the equations to find az/əx and əz/ðy. e? = 8xyz %3D az 1 1 az ay %3D y

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Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: 2 HA=A-tj + (t – 1)k, B = 271 + 6Ak, find (a) (A - B) dr %3D

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: Which conclusion does the diagram support? ZY A. %3D XX MA В. %3D M- XNM C. O D. VY = W X

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Q: Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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Q: (b) Oppositely directed to 18i – 12j + 6k. - 3 i 1 j + k V6

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Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

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Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: In the diagram below we have that ST B = 69° and CDU = 62°. %3D %3D E A S -V U Find: 1. ВСТ 2. ABT =…

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Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Find V· (V × F), if F(x, y, z) = 7e*²i+ 6xe"j –- 6e²k. V·(V × F)

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Q: Find r(t) for the given conditions. r'(t) = 8ei + 9e'j, 9efj, r(0) = 2i %3D r(t) =

A: We have,  r'(t) = 8e4t i + 9et j   r(0) = 2i We need to determine the value of r(t)  Integrating…