If u = 5i + 2j, v = i - j, and w = 3i - 7j, find u . (v + w).

Q: Find the indicated quantity, assuming thatu = 5i + j, v =i - 3j, and w = 31 + 4j. + v) (u v)

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Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

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: Find the indicated quantity, assuming that u = 5i + j, v =i - 3j, and w 3i + 7j. %3D %3D u (v + w)

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Q: dA, R = {(x, y) : 0 < y< 1,0 < x < 2VI} xe

A: As per the question, we will be evaluating the integral ∫01 ∫02y xe-y2dx dy. So,…

Q: Find the indicated quantity, assuming that u = 7i + j, v = i − 3j, and w = 3i+2j.     u · (v + w)

A: Compute v+w as follows.

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: 8. Given: u = 8i + 6j and v= 3i – 4j. Determine if u is perpendicular to v.

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Q: Find the indicated quantity, assuming that u = 5i + j, v = i – 3j, and w = 3i + 6j. u (v + w)

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Q: H.W. 1 Given that zl = 3 + 4i, z2 = 1 – 2i, calculate: %3D 4. 22. 21 5. zl+3 6. 2* z2

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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: Given u= 7i + 9j and v= 5i – 10j, find u V. %3D - - Give your answer in the form ai + bj.

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Q: Consider A = 8i – 12j, B = 2i + 14j, and C = 18i – 10j. %3D %3D

A: See attached file for a step by step explanation.

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

A: First, we calculate v+w ,then take dot product with u .

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j, v = j + k

A: Given: Two vectors are . In part (a) Find the vector product of two vector u and v. therefore the…

Q: If X and Y are independent RVs, then E(YIX) - F(Y) nd F(Y10

A: X and Y are independent then joint distribution of X and Y is  f(x,y)=f(x)f(y)

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: Let u = 4i + 7j and v = 7i − j. (b) Find the component of u along v. i put 2.97 but it says it is…

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

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Q: For v = 2i - j and w = i + 2j, find the dot product v . w

A: We know that, the dot product of two vectors  a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ is given as…

Q: r'(t) = 12e6ti + 7ej, r(0) = 2i %3D %3D r(t) =

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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: If u=2i + j -3k and v=i + 4j +k, find u x v.

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Q: Let a = ci + jand b = 2i + 14j. Find c so that a and b are orthogonal. i

A: Given that,a=ci+j and b=2i+14j

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: Find the indicated quantity, assuming that u = 2i + j, v = i − 3j, and w = 3i + 7j. u · (v + w)

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Q: Given u = 3+ 2i, v = –1+4i, compute ūv +

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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: If a = 4i + 2j + 4k ,b = -2i + 4j – 3k and č = 4i + 5j. If å + xb is perpendicular to č then find x.

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Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: Show correct answer from the multiple choice options.

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Q: If z = u sin(u?) and u = Vt, find ) If z = x² + y², x = u+ v² and y = u² – v, find and

A: Given: (a) z = u sin ( u2 )  (b) z = x2 + y2  , x and y values given

Q: If VW = -2z + 29, UX = z + 9, and ST = z + 13, what is UX? %3D V U UX w/ ト

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Q: Find u x v, v × u, and v × v. u = 6i + 8k v = 3i + 8j – 4k. (a) u x V (b) (c)

A: This question is based on cross product.

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: Given u = 4i - 3j and v = -6i + 4j, calculate u· v.

A: See the attachment

Q: Let a ci + j and b 2i + 6j. Find c so that a and b are orthogonal. C =

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

A: Given:          v=3i-6jw=i+j Using the component formula for the dot product of two-dimensional…

Q: Bef(u, v) = uv and v calculae %3D + vu- dvðu?

A: To find- Be fu, v = uv and v calculate u∂3f∂u3 + vu∂3f∂v ∂u2.

Q: Find the indicated quantity, assuming that u = 4i + j, v = i − 3j, and w = 3i + 2j. u · v + u · w

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Q: (x, v) = (2ry) i + (r – 2rv) j ,2]. -

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Q: 8. Given: u = 8i + 6j and v = 3i – 4j. Determine if u is perpendicular to v. %3D

A: Two vectors are perpendicular if there dot product is 0

Q: ux v of u = 2i + 3j, v = -i + j is *

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Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

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Q: Find the cross product (-2i – j+ k) × (–3i – j – k).

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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: 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: Let u = 4i + 7j and v = 7i − j. (b) Find the component of u along v. (c) Find projvu.

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