7. Let u = (-4, 2, 3), v = (5,0, –7), and w (7,-2, –5). Find the components of (a) -u + (v – 3w) (b) (4v – w) – (4u + v)

Q: If z1 = (3,7) and 22 (5,-6), then 2122 is equal to what? %3D А. (57, 17) В. (15, - 42) С. (15, 42)…

A:

Q: Find u − v, 2(u + 3v), and 2v − u. u =  (6, −7, 8, 3),       v = (−2, , 7/3, −8/3 , −1)

A:

Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

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

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: Let u = 4u + 5v (9, -2, -8) and v = (4, −3, −1).

A: The required solution is:<56,-23,-37>Explanation:

Q: Show that the equation (1, 2, 3) × v = (−1, 2, a) has no solutionfor a = −1

A: Consider the given: Given equation:1,2,3×v=−1,2,aLet v=x,y,z1,2,3×v=ijk123xyz…

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (1, −2, −3), v = (3, 1, 0)

A:

Q: (2 + j)?

A:

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: Calculate v × w, where v = (−2, 1, 4) and w = (3, 2, 5).

A: Given: v = (−2, 1, 4) and w = (3, 2, 5)

Q: Find dy2 of z = 2x – 5xy² + x² y° %3D -

A:

Q: let v = (−2, 5) and w = (3, −2) Calculate 5w − 3v and 5v − 3w

A: Consider the given vectors. v=-2,5w=3,-2 Now, find the value of the vector 5w − 3v.…

Q: Find (3u − v) ∙ (u − 3v) when u ∙ u = 8, u ∙ v = 7, and v ∙ v = 6.

A: Given, u ∙ u = 8 u ∙ v = 7  v ∙ v = 6 To find:   (3u − v) ∙ (u − 3v)

Q: Let z1 = -5 + 14i and z2 = 5 – i. Find z122 and (z1z2). 7122 (2122) ||

A:

Q: = (2xy + z² )i + (x² +z)j + (y + 2xz)k, determine a possible value for .

A:

Q: Find

A:

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −2, 4), v = (1, 5, −3)

A:

Q: 1 (45) + C₂ (²³) + C3 ( ²₁ ) = Figure out constants C₁, C₂ and c3 such that c₁ 0.

A: A detailed solution is given below.

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −3, −3), v = (3, −3, 3)

A: Given: u=(3, −3, −3), v=(3, −3, 3)

Q: z =3−4i

A: Now conjugate of z is,

Q: 2a - 5y dA, R =(-5,4] x [0, 3] R.

A:

Q: Find the difference between BC and CA where A (1, 2, 3), B (3, -1, 4) and C (-2, 3, -4).

A: Given A=(1,2,3) B=(3,-1,4) C=(-2,3,-4)

Q: Find the center and radius of each circle.

A: Center is (-1,-6) with radius 4

Q: Find (u + v) ∙ (2u − v) when u ∙ u = 4, u ∙ v = −5, and v ∙ v = 10.

A: u·u=4,  u·v=-5  &  v·v=10