find u ·v. u= [ 1,√2,√3, o],v= [ 4, -√2,0,-5]

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

A: This question is related to vectors, we will solve it using given information.

Q: Find R f(x, y) dA where f(x, y) SIR f(x, y) dA- = x and R = [0, 4] × [-2, 4].

A: Given f(x, y) = x and R = [0, 4] x [-2, 4]

Q: Find the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

A:

Q: E (u, v) = (u – v², u² + 1, v²) |

A:

Q: Please solve

A:

Q: Let f(x, y) = x² – xy + y? – y. Find the directions u and the values of Duf(1, –1) for which %3D…

A: Explained below

Q: Find w such that 2u + v- 3w = 0. %3D u = (0, 5, 7, 2), v = (-3, 4, -8, 1) W =

A: vector

Q: f Vf(x, y) = 0, then Duf(x, y) = 0 for all u. %3D %3D

A: True

Q: 2. S → (T → U) U → -U (V → S) ^ (W → T) .. V → ~W

A:

Q: Find u•v

A: As   u = -12,2         v = 1,6   So,  u→=-12 i+2 j        v→= i+6 j

Q: Find u x v, v × u, and v × v. u = i - j, v=j - k V (a) u x v (b) v x u (c) v x v

A:

Q: Find a linear transformation T:

A: Consider the provided information, T11=23   and T1-1=05 Find a linear transformation T. We can put…

Q: Let f(x, y) = x2 – xy + y² – y. Find the directions u and the values of Duf(1, –1) for which Duf(1,…

A:

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

A:

Q: 8. Use change of variables to find: a) The Jacobian if x=(u+3v), y =; -(v- 2u).

A: We will use concept of change of variables.

Q: x = u - v2, y = u + v (x, y) = (u, v)

A: Given , x = u - v2 , y = u + v

Q: Let f(x, y, z) 75 Then Vf = and Duf(1,3, -3) in the direction of (-1, -2, -2) is

A: Given the function

Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F) = (4(y+2), 4:x, 0)

A:

Q: af Find if f(x,y) = ysin xy

A:

Q: Find ||u||, ||v||, and ||u + v||. u = -2, V = 5, (a) ||u|| (b) ||v|| (c) ||u + v||

A:

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

A:

Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

A:

Q: Find u· (v X w). 22. u = (1, -2, 2), v = (0, 3, 2), w = (-4, 1, -3)

A: Given that  u=(1,-2,2) v=(0,3,2) w=(-4,1,-3) To find u.(v*w)

Q: b) If x = u(1 + v) and y = v(1+u), find vx, Ux and a(u,v) a(x.y)

A:

Q: Find r' (2), where r(t) = u(t) × v(t), with u(2) = (1, ,2, – 1), u' (2) = (3, ,0, 4) , and v(t) =…

A: Solution :-

Q: Find the distance between u and v.u = (1, −1), v = (−1, 1)

A:

Q: ... Solve for w where u = (-1, 1, 1, 0) and v (-1, 2, 3, 0). 3w = u- 4v W 3=

A:

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

A: We will find out the required values.

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: Express w as a linear combination of u and v. 1 - 5 u = V: w = - 9 w = u+

A:

Q: Find u x v, v × u, and v x v. u = 2i + 9k v = 4i + 6j – 3k. (a) UX V (b) (c) V X V

A:

Q: Find 2 (v x u), given u x v = (-, 5, 8). %3D

A: u×v=-83, 5, 8

Q: Find projy u. v = 7i-3j+ k, u = -4 j+ 3 k 60 45 j+ k 59 59 O 105 i- 59 45 15 k 59 59 9 9. +k

A:

Q: Find u × v, v × u, and v × v. u = 4i + 8k v = 4i + 8j – 4k. (а) ихv (b) v × u

A: We have to find

Q: Find (u, v) for (u, v) = 2u,v, +3u, v, +u,v, defined in R, where u (9,0,-3) and v (8, 2,17). A. (u,…

A:

Q: Find u-v. u=-3i+2j, v=4j

A:

Q: Find the length and direction (when defined) of u x v. u = -,i + +k U = i + j + 2k ||uxo ||= 8 | ||u…

A:

Q: Find proj y u where v= i+j + k, u = 12 i +3j+4 k O 20. 20 20 j+ k O 19 w/ 19 19 k i + j+ O 19 19 169…

A:

Q: Find f'(2) where f(t) = u(t) v(t), u(2) = (1,2, –1), u'(2) = (3,0, 4), and v(t) = (t, t2, t).

A:

Q: Find real numbers x, y and z such that (а) (b) 7xi + (y – 3)j + 6k = 10i + 8j – 3zk (x + 4)i + (y–…

A:

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

A:

Q: Find Cov(X, Y)

A: Covariance: It is a statistical measure used to establish a relationship between two random…

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

Q: f(x,y)=21 (x+y), x=1,2,3, ; y=1,2 0 , d.d.

A: Given :- fx,y = 121(x+y)        x=1,2,3 and y=1,2 we have to calculate cov(x,y)     Formula:- Covx,y…

Q: Find u x v, v x u, and v x v u = i+j, v-j-k (a) ux v (b) v xu (c) V X v

A:

Q: Find Duf at P. 2. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i+ 1 Duf = i

A: We need to find directional derivative at p.

Q: The dot product of u = ⟨u1, u2⟩ and v = ⟨v1, v2⟩ is u ∙ v = ________.

A: Dot Product: The vector is u=(u1,u2)v=(v1,v2)u=u1i+u2jv=v1i+v2j

Q: et V xu u = (1,3,-3), v = (4,0,2) e l -3 %3D ......

A: Given:            u=1,3,-3            v=4,0,2 The cross product of two vectors is…

Q: - gt V Xu u = (1,3,-3) , v = (4,0,2) e l

A: The given vectors are: u=(1, 3, -3)v=(4, 0, 2)

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.