(20) If Ø is scalar function and A is vector function, then V· (Ø A) = Ø (V · A) + A VØ is (a) Ø (V· A) + A•VØ (b) Ø (V · A) (c) A· VØ (d) None of these.

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: Find vector c × (a + 3b), where a, b, and c are given below. ijk i j k -1 a = 509,b=0 0 1 0 -9i+27i…

A:

Q: Question 6 Let A' = [-4 16 8] and B' = [-1 x² 21 For which real value(s) of x are vectors A and B…

A:

Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: Let u, v be unit vectors and c ∈ R be a scalar. Use the fact that Dvg(a, b) = ∇g(a, b) · v to show…

A:

Q: 4 В T(t+h) A 21 y 01 2

A:

Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

A: Here 2 different problems are provided. As per our Bartleby Guidelines, we are supposed to…

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: 3. Which vector is not equal to zero? a) ix (j×k) b) (ix j) × k c) (i × i) × j d) ix (ix j)

A:

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

A:

Q: (a) Suppose A=(S,+S) and B (S-S), Show that S = A + B A= A and B =-B (b) Suppose that A B, is a…

A:

Q: Can a vector in a vector space R -4 - 2 be 2. span by -1 2 イ

A: Span of vectors.

Q: For any vector A,ix (i x A) +jx (j xA) + kx (k xA) = -2A ylan O İhi O

A: We use vector triple product to answer the given question.

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

A:

Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

A:

Q: (a) Given that V= əx ə a i+ j+ -k. Show that V.VB=V²B where is a scalar ду əz (b) If M and N are…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: (7,1, –4, –2,3). Find the components of the (a) Let u = (1, 2, –3, 5, 0), v = (0,4,–1,1,2), and w =…

A: Let u→=1+2j^-3k^+5l^      v→=4j^-k^+l^+2m^      w→=7i^+j^-4k^-2l^+3m^Given:-…

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

Q: But for any vector A and scalar V, the identity or V VA = A.VV + V(V-A) (VA) V = VVA - A VV

A:

Q: Use the table to answer the following question. Number of Half-Lives 1 2 3. Remaining Amount of…

A: Exponential function

Q: Question Two (a) Prove that the vector field F(x, y, z) = (x² + y²)i – 2y(z+=)j + (zy +2²)k is…

A: The given vector function is, F=x2+yzi-2y(x+z)j+(xy+z2)k. To Prove: this vector field is…

Q: Let T: R2 R³ and u, v E R2 such that T(u) = 1 2 -2 and T(v) = 4 -2 1 Find the image under T of the…

A:

Q: CHCR) and C= Let B= - 3 of vis [v]B 1 1 [;)] 3 = A [v] 0 M-[2] 3 ⓇM1.- [³] B [v] = 0 0 4-A] -9 Ⓒ…

A:

Q: (1) Let x and y be the vectors x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z is…

A: