If v = (3, – 1, 1) and w = (-2, –2, –2) , what is v x w ?

Q: Find f,, fy, and f,, and evaluate each at the given point. X' 'y' fx, у, 2) 3 х*уз + 2хyz - 8yz,…

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Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v= (6, 9) a = b =

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Q: If ø = Vx + y+ z and ū = 'î + ĵ+ k , then V¢.ũ will be 3 V3 20 2ф

A: Step:-1 Given that ϕ=x+y+z, u→=i^+j^+k^ ∇→ϕ=∂∂xi+∂∂xj+∂∂xk x+y+z ∇→ϕ=12x+y+zi +12x+y+zj…

Q: Given f(x, y, z) = v- 5x – 3y – 4z, find fa(x, Y, z) = f,(x, y, z) = f:(x, y, z) =

A: Given,          fx,y,z=-5x-3y-4z

Q: For v = (1, 4), w = (3, 2), calculate:(a) v + w (b) 5v

A: We have been given that v=(1,4) and w=(3,2)Our Aim is to calculate:-(a) v+w=(1,4)+(3,2)=(1+3,…

Q: Show that S is a basis for V = span(S).

A: We are given,  We need to show that S is a basis for V = span(S). In other words, we need to show…

Q: If P(x) = 15' X = 1, 2, 3, 4, 5 = 0, elsewhere %3D Find P(X = 1 or 2)

A: Answer: From the given data,

Q: If|u|= 3 and|v|= 6, find|u×v|and whether u×v points into or out of the page.

A: If|u|= 3 and|v|= 6, find|u×v|and whether u×v points into or out of the page.

Q: Suppose that A = {1} and B = {u, v}. Find A x B. Find P(A x B) .

A: Here the given sets are                                   A={ 1 }…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t).

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Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: Given that v = and w =. Find

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Q: If ||u|| = 2, ||v|| =√3 , and u x v = 1, find ||u + v||.

A: Given that u=2,   v=3   and  u*v=1. This implies that,

Q: Let f(x, y) = x²y³, then Vf(1,2)= Select one: True False

A: Given problem:- fx,y=x2y3 Then ∇f1,2=16,12?

Q: o Find the Vf at the given point 4. If f= 2ryz and g=ry+z, fing V (f+g) and ▼ (fg) at the point (1,…

A: Given:       f=2xyz       g=x2y+z      f+g=2xyz+x2y+z           ∇f =∂f ∂x,∂f∂y,∂f∂z

Q: T. If TM 3y and TX 2y + 24, then Y

A: Given,  TM = 3y TX = 2y + 24

Q: calculate r'(t) and T(t), and evaluate T(1). r(t) =〈3 + 4t, 3 − 5t, 9t 〉

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Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: Given: u = (-1,3), v = (2,4), & w = (2, –5), find each of the following: а. и + v b. 2w – v С. Зу —…

A: Given: u=-1,3, v=2,4, w=2,-5

Q: Given that A and B are independent with P(A ∪ B) = 0.8 and P(B c ) = 0.3, find P(A).

A:

Q: Given that =, = [3,0.7]. -2 = [2. 1.2] and =; = [4,-0.5]. (a) find xz, and z, x z3 (b) show that [1,…

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Q: If x I y and y I z, then b

A: For the lines l, m & n, if l∥m & m∥n, then from transitivity rule l∥n.

Q: find the value of a for which       [ 4 ] v = [ a ]       [-4]       [ 3 ] is in the set…

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Q: Let T ∼ Γ(r, λ). If μT = 8 and r = 16, find λ and σ².

A: It is given that, The value of λ is, Thus, the value of λ is 2.

Q: For what values of c is the set {t +3, 2t +c2 +2} linearly independent?

A: The given set: t+3,2t+c2+2

Q: If z = xye», x = u · 3“, and y = u · v², find dz when u ди 2 and v = 5.

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (c) z = x2 + 2y2 ; x = es - et, y = es + et

A: Formula to find the partial derivatives helps to find the partial derivatives of the function with…

Q: r(0)=, find v(t) and r(t).

A:

Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v – w + 3z = 0. z =

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Q: Given that D/d = √f + p/f – p, express p in terms of f, d and D

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Q: Find a and b such that v = au + bw, where u = v = (7,2) a = b || || = (1, 2) and w = (1, -1).

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Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: If f(u) : f'(u) = V13 + w'dw then

A: Let,

Q: : Given a r.v.*=2, 3,4,5, then Find the Pif. of X (fw): ,

A: Given that, a  random variable , X = 1,2,3,4,5 We need to find probability function of X i.e f(x)

Q: You are told that Vf(2,3) =. %3D Given ü =, compute Düf(2,3).

A:

Q: 2. Given V = x + y' av a) Find and b) Hence, show that y ( - ) = v. = V. ду

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Q: if Vx + a = b , then x=

A: Given x+a3 = b We solve the equation by doing the cube both sides and then applying the mathematical…

Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: Given: if fx,y,z=x2y2z2 then fxyzx,y,z=2xyzx2y2z2 We have to state if the given statement is true or…

Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and du…

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Q: Let ř =xi+y+ zk, and let u= ||F|I. 2-2u = 3ue. Show thet Dflu)= 6- 6u)e" r.

A: Given, fu=3u2e-2u. We have to show that ∇fu=6-6ue-2ur→ where r→=xi^+yj^+zj^.

Q: If f(z) = z² - (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: For what value(s) of h will y be in Span{v1, v2, V3} if 5 -3 -4 V1 V2 -4 V3 and y = -7

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Q: Given f(u, v), where u = x² y, v = xy? If at the point (2,3), f, = 4, fm = 3, fm = 5, ƒ, = 1, fm =6.…

A: Given; u=x2y, v=xy2

Q: Find f, and f, and evaluate each at the given point. f(x, y) = e*y?, (In 9, 2) f(x, y) = 5,x, y) =…

A: We have to find the first partial derivatives of the given function.