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

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

A:

Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: Find (a) u x v, (b) v x u, and (c) v x v.

A:

Q: let U = 5i +12j, V =24i + j, and W = i - 4j, and find:   |2V-U|

A: U=5i+12j, V=24i+j and W=i-4j

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

A:

Q: Given u(x, t) =t=?e, compute: e 2t

A: We have to calculate uxx of the given function.

Q: If w= Xze' y=va²–x² , z=Sirx, then ( dw is

A: we will derivative by using chain rule

Q: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

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: Given M = {(x, y), 1 < x² + y² < 4}c R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: See the attachment

Q: For which value of x is p = (1,0, x) orthogonal to ā q = (10,3, –2 )? %3D 5.

A: Solution:- step:1      ∗vectors are  orthogonal if the dot product of the  two vector          is…

Q: 1. Let u = 2î + j- 2k, v = 12î – 4f + 3k and w = 4f + x?k c. Find x such that u and w are…

A: u = 2î + j- 2k, v = 12î – 4f + 3k and w = 4f + x?k

Q: Find the Jocobian for x = u + vw, y = v + wu, z = w + uv

A:

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

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

A: As we know a×b = - b×a

Q: Find u x v, v x u, and v X V. u=i-j, v=j-k

A:

Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: Find the uncertainty in U, assuming that X = 10.0 ± 0.5, Y = 5.0 ± 0.1, and a) U = XY² b) U = X² +…

A:

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

A: According to the question, we have to find the value u·v+w, if u=5i+2j,v=i-j and w=3i-7j. The above…

Q: Given u(x, t) = t°e¯ï, compute:

A:

Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D

A:

Q: Show that for all u e V, [T(u)]c = A·[u]g. Hint: For i = 1.r, find [T(v¡)]c and then, write u =…

A: Given that . For , V⊆ℝn and W⊆ℝn , V,W are vector subspaces and β=v1 , v2 ,...vr and C=w1 , w2…

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

A:

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

A:

Q: If u -x2 + y? + z² be such thatr u,+ yu, + zu̟ = Àu, then A is equal to %3D + A.1 В.2 C.0 D. none of…

A: Given that, u=x2+y2+z2 Then xux+yuy+zuz=λu The aim is to find the λ value, ux=2xuy=2yuz=2z

Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

A:

Q: Suppose u=, v=x +y and w w(u.v): a) Express W and W, in terms of W. . X and y b) Calculate xW, +yw,…

A:

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

A:

Q: Solve for w, where u = (1, −1, 0, 1) and v = (0, 2, 3, −1). w + u = −v

A: Let's consider w = (a, b, c, d) So w + u = (a, b, c, d) + (1, -1, 0, 1) = (a + 1, b - 1, c, d + 1)

Q: If X and Y are independent RVs following N(8, 2) and N(12, 4/3 ) respectively, find the value of 2…

A:

Q: Be z = (x-y)/(x+y), where x = (u/v), y = (v2/u), calculate ∂z/∂u and ∂z/∂v

A: The given equation is z=x-yx+y where, x=uv, y=v2u. Find the value of ∂z∂u and ∂z∂v. Here we use the…

Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

A:

Q: Given: z = = x* + zy°, * = ww* + w, y = u +ve" a z Find when u = - 3, v = 2, w =

A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

A:

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v= (4, 5) a = 3 b = 1

A:

Q: let U = 5i +12j, V =24i + j, and W = i - 4j, and find:   U.W

A:

Q: Show that if X and Y are independent rv's, then E(XY) = E(X) · E(Y)

A: we have given that, x and y are independent random variables, then, we will prove, E(XY)= E(X).E(Y),

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

A:

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). v = (0, 24) V = a = b =

A:

Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Given, o (x, y, z) = 3x²z – z²y³+ 4y°x² – 2y + 4z – 1, find V²¢. O 6z + 6y3 – 6z²y+ 24x²y 6x 12z +…

A:

Q: If u= 2i +3k and v = j– k, then

A: We will use formula for cross product of two vectors

Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

A:

Q: If z xy? +x°y, find zZxxy and Zyxy %3D

A: On doing partial differentiation we will get

Q: If a = i + j + 5k and b = i + j + 3k, compute the cross product aXb

A: We have to find cross product