Let v=4i−j+k and w=2i+3j−k. Find (a) a scalar s so that v is orthogonal to v−sw (b) a scalar ss so that sv+wsv+w is orthogonal to w

Q: Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

A: We have to find the scalar product a·b when (i). a=x+2y-z and b=2x+3y+z(ii). a=x-3y+z and b=2x+y+z

Q: ) Show that F = (2xy +2³) i+x²j+3r2²k is conservative force field. Find the scalar potential of F.

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: (a) Show that the vector field F(x, y) = (x², y²) is conser- vative, then find the potential…

A:

Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

A:

Q: (a) Prove that if u is orthogonal to both v and w, then u is orthogonal to v + w. (b) Prove that if…

A: Given: (a) If u is orthogonal to both v and w. To prove:  u is orthogonal to v + w. (b) If u is…

Q: 2 3 Let A = L and U -2 Find scalars s and t so that LU = A.

A: First, find the value of LU. LU=20t-2130s=2· 1+0· 02· 3+0· st· 1+-2· 0t· 3+-2s=26t3t-2s

Q: Find the scalar a nd b such that v = au + bw where v = 4,3 ; u = 2,5 and w = 1,4 PLEASE SHOW STEP BY…

A: Answer and explanation is given below..

Q: (2) Find the real values of a,b.c that make the convolution equal to zero for the vector function…

A:

Q: Consider the kets: -3-2i] Irn) = -6i 5i [4i-71 ,Ir2) =9+8i y Ir3) = 4-5i [7i-4] 3 11 a) Calculate…

A:

Q: Masses of 3 kg, 1 kg and 5 kg are located at points with co-ordinates (1,2). respectively.

A: Please refer to the image below

Q: 1-If č=ÅxỂ where Ã= 3L- 4J and B= -21 + 3k what is C? 2- Find the scalar nroduct i E of the two

A: Note: " Since you have posted multiple question. As per our guidelines we are supposed to solve one…

Q: Let A=[ Let B=A -t| 3. -2 where t is scalar, Fao which velve (s) of t is B singular?

A:

Q: Determine a scalar equation for the plane that passes through the point (2, 0, -1) and is…

A:

Q: Let v e R? be a vector in the first quadrant. Express v in terms of its coordinate vectors with…

A:

Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

A:

Q: Let p.v. z1/2 denote the principal branch of the complex square root. Compute p.v. 21/2 dz, z +i…

A:

Q: Find the flux of the vector field V(x, y, z) = 9xy²i + 9x²yj + z³k out of the unit sphere.

A:

Q: The line of action of the 4800-lb force F runs throu the points A and B as shown in the figure.…

A: The scalar component a→ along with b→ will be:                     Compb→a→=a→.b→b→…

Q: Consider the scalar field f(x,y, z) = 2x² – y² + 3z? Determine V Vfl(1.-1.1) II. VxVfl1.-1.1)

A: Here, the given function is: f(x,y,z)=2x2-y2+3z2

Q: v.(OF = (vo) - F+o(V .F (V) F+

A:

Q: For the vector field F = ((y/z2+1)i + (-2x/z2+1)j + (3x2+3y2/(z2+1)2)k , calculate curlF

A: We have given vector field F=yz2+1i+1-2xz2j+3x2+3y2z2+12k=yz2+1,1-2xz2,3x2+3y2z2+12=F1,F2,F3…

Q: Violet now comments that there are scalars a and B such that di DE = a EF × EG = B GF x GD State the…

A:

Q: Let v ∈ R2 be a vector in the first quadrant. Express v in terms of its coordinate vectors with…

A:

Q: Determine a scalar r such that Ax = rx, where 1 A =| 1 1 and x = 4 -4 5

A: Ax=r x ⇒ x is an eigenvector of Afor the eigenvalue r. So to find r, we compute all the eigenvalues…

Q: The inner product of anti-symmetric and symmetric tensor is а. 1 b. 0 С. -1 d. none of the above

A:

Q: Determine the vector field of F. F(x, y) = 4i – 2j

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 1. Let a force F be given by F = Fo(i+ 4j + 8k) where Fo is a constant. Determine the scalar…

A:

Q: Consider the scalar field f(x,y, z) = 2x² – y² + 3z2 i. V Vfl(1.-1.1) Determine II. VxVfl1.-11)

A:

Q: ey are linearly dependent, find scalars a, b, and c, not all zero, such that au + bv + cw = 0 u =…

A:

Q: Find the gradient of the following scalar fields: a) F=x^2+y^2 b) V=p^3z cos2phi

A:

Q: The projection of y onto i is a scalar multiple of y.

A:

Q: Find the net outward flux of F =axr across any smooth closed surface in R, where a is a constant…

A:

Q: Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0),…

A:

Q: If f(x) and g(x) have a period p, show that h(x)3Da f(x) + b g(x) (a, b constants) has the period p.…

A:

Q: Sketch the vector field F = (5x.4y - 5x). Choose the correct answer below. O A. OB.

A: Given query is to find the correct option for the vector field of F.

Q: 1) a) Let u= and v=, where c is an undetermined scalar. What value should c have if u is to be…

A:

Q: Calculate ∇φ and ∇2φ of the scalar field: φ = e √ x^2 + y^2 + z^2

A:

Q: Compute the metric tensor g and the matrix L representing the Second Fundamental form, X (u, v) =…

A: Given that X(u,v)=lncot u2-cos u,sinucosv,sinusinv Where u,v∈0,π2×0,2π Take the derivative for u,…

Q: Determine a scalar r such that Ax = rx, where 1 A = and X=

A: Given, A=2112, x=11

Q: (b) Find the scalar potential of the conservative field: F = 2ry°z?i + 3x²z²y²j+ 2x?y³zk. %3D

A: Let's find.

Q: Denote three scalars A = eTE-le, B = µTE-le and C = µTE-'µ. 1. Prove that AC – B² > 0.

A: We are given three scalers A,B,C in terms of weighted matrix inner-products, and we have to prove…

Q: Determine the vector field of F. (x, y) = 12i – 4j 1

A: given isF(x,y)=12i-4jgraph of vector field of F is attached below

Q: Let f: C → C be differentiable at zo. Considering f as a map R? → R², that f'(zo) = kR where k is a…

A: (a)

Q: 1. Let R? have the inner product of Example 1, and let x = (1, 1) and y = (5, – 1). a. Find ||x||,…

A: Let R2 have inner product s.t.if u= u1,u2 and v=v1,v2 betwo vectors in R2then &lt;u,v&gt;=u.v…

Q: Find a scalar equation of the plane that passes through the points (1, 1, 1) and (2,0,3) and is…

A:

Q: Find all scalars c, if any exist, such that i+ cj + (c – 3)k is in the span of i+ 5j + 2k and - 5i +…

A: To Find: All scalars c, if any exist    such that i→ + c j→ + c-3 k→ is in the span of i→ + 5j→ +2…

Q: Show that the vectors u = (1+i, 2i) and w= (1, 1+i) in C² are linearly dependent over the complex…

A: The vectors u and w are linearly dependent in K2 (with K = ℝ or ℂ), if there exists a,b∈K with a=b=0…

Q: Compute the flux of the vector fieldi = -3 i+ 4j- 2 k through the rectangular region shown below,…

A:

Q: Determine a scalar r such that Ax = rx, where

A: