Find the value of β for which w =〈−2, β〉 is parallel to v =〈4, −3〉.

Q: For which value(s) of s, if any, v1, Let Vi V3 S 1 V2 and v3 are linearly independent.

A: For linearly independent, mode of matrix of vector is zero.

Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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

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Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i + 2j − k, v = i + j + 2k

A: Given vectors are (a)

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 3t³i + 6tj - t²k (a) r(t) (b) r"(t) (c)…

A: Given data÷

Q: Find the linearization at the point indicated:   V (h) = 4h(2 − h)(4 − 2h), a = 1

A: Given: Vh=4h2-h4-2h ,a=1

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: Hw÷ find the Voctor Peralle I to the line intersedbetween the two flane 3X-6y-2Z=5 and 2x+4-27=5

A: The equation of the given planes is, 3x-6y-2z=52x+y-2z=5 If n1 and n2 are the normal to the planes,…

Q: Given the function g(x, y, z) = x²y - 4zex+y, find the slope at P(1,0,1) in the direction of the…

A: Here is the solution

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: Find the value of c such that P(Z > c) = 0.28 %3D O a. 0.3 O b. 0.58 O c. 0.85 O d. 0.22

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Q: Suppose that VX=14.4, VW= 36, and VZ= 12. Find XY. %3D W XY = %3D

A: From the given figure

Q: iven T: R2 -> R2, where T(x,y) = (x,y2), Is T linear? Explain.

A: Given: To explain the given statement as follows, R2 + R2, where T(x,y) = (x,y2).

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: Let x be the r.v Such that ECx)=D2 ECx)=2a %3D [2+Qx}?) =2a3 %3D Findthe Value of a

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Q: B- Let r(t) = (²+2) i + (3t) j .Find (t) such that r(t) parallel to r'(t).

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Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: Find the cross product a x b. a = (9, 0, -4), b= (0, 9, 0) Verify that it is orthogonal to both a…

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Q: Calculate r'(t) and r"(t) for r(t) = (t, t 2, t 3).

A: Given:        r(t)=⟨t,t2,t3⟩

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 u x v. u =j + 4k, v = 2i - k Show that u x v is orthogonal to both u and v. (u x v) • u = (u x…

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Q: Let f(z) = x? + iy² where æ and y are the real and imaginary parts, respectively of z and C is a…

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Q: Find the directional deriyative of f(x, y)=y In x at the point (1, 4) in the direction of V=-3i +…

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Q: Use the Chain Rule to find dw/dt. w = xevlz, x = t, y = 4 -t, z= 9 + 2t 4xv dw 7,6 dt

A: Given that      w = xey/z , x = t7 , y = 4-t , z= 9+2t Here we have to find  dw/dt

Q: ut (X, Tof) be the cofinita to p. Jet A = {1,3]. etス=R B= Co1) %3D Fnd Ā ļ B.

A: Here given that X=R  Let A={1,3} and B=(0,1)

Q: Determine values of x and y so that v · w = 0 and v · u =

A: There are vector representation given as, v=x1y , w=x-20  and u=0-9y. To find the value of  x  and y…

Q: Which of the following are first order linear aiterential equations? F. = y – 3y

A:

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: 10. Given R = x7 + y3+ zR, and r = |R show that (a) V x (7 x R) =7 + 7R, (b) (A x V) × R = -27, (c)…

A: Given: be any constant vector.

Q: Let f(z) = x? + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A:

Q: Determine the real number \( \alpha \) u x v and î are orthogonal, where ù = 3î + ĵ– 5k and v = 4î –…

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Q: Find r(t) u(t). 1 r(t) =D (5t-7)i + 하 + 2k %3D u(t) = t²i – 4j + Pk %3D r(t) · u(t) = %3D

A: Vector Question

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: Find u x v. u = j + 3k, v = 7i - k Show that u x v is orthogonal to both u and v. (u x v) · u = (u x…

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Q: Find the cross product á xb and verify that it is orthogonal to both á and b for á = i+ 33 – 2k and…

A: Given:-a→=i→+3j→-2k→b→=-i→+5k→To find: cross product a→×b→

Q: Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property…

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Q: find the distance d(u, v) between u and v in the given exercise.

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Q: Given r"(t) = , r'(0) = and r(0) = < 3, Find the j-component of r(6). %3D %3D %3D

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Q: Use the Chain Rule to find dw/dt. w = xevlz, x = t, y=7 - t, z = 5 + 7t dw dt

A: To find the derivative using chain rule

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j − k, v = 2i + 2j + 2k

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Q: Consider P2 with the inner product . = f(x)g(x) dx. Then d(r, 1) = %3D a) b) V3 d) 1 e) 13

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Q: Find r(t) u(t). r(t) = (5t – 4)i +j - +2k 2. %3D u(E) = i - 4j - ēk %3D | r(t) u(t) -

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = – 2tj %3D

A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: Consider P2 with the inner product = | f(r)g(x) dz. Then d(r, 2): %3D a) V b) d) VA c) 2 e)

A: Explanation of the answer is as follows

Q: Find r(t) if r'(t) = t4 i + e' j+ 3te3t k and r(0) = i +j+ k. %3D r(t) =

A: Given, A vector r'(t) = t4i + et j + 3te3t k and  r(0) = i + j + k.

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = 2i + k, v = i + 3k

A: Given that, the two vectors u = 2i + k, v = i + 3k To find the following (a) u × v, (b) v × u, and…

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

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Q: Find V (F x G), if F(x, y, z) = 11xi+j+13yk and G(x, y, z) = xi + yj – zk. %3D V. (F x G) =

A: Given,            Fx,y,z=11xi+j+13yk and Gx,y,z=xi+yj-zkTo find : ∇·F×G