Find u x v, v x u, and v x v. u = 2i + 6k v = 5i + 9j - 2k. (a) -54i + 22j + 18k u x V (b) V x u 54i - 22j - 18k (c) 0 VX V

Q: Integrate the given expression. [(4x + 2)2 dx A 16 x 3 + 8x 2 + 4x + C 3 B) 32x+ 16 + C (c) 16x 3 +…

A: ∫4x+22dx =∫16x2+4+16xdx =16x33+4x+8x2+c

Q: Find each of the following. a = 2i +j b = i - 4j (a) a + b 3 i+ -3 (b) 4a + 5b X i+ -15 |× j 6. (c)…

A: A detailed solution is given below.

Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Given the vectors v=i−4j+2kw=3i+2j+k

Q: Find u x v, v x u, and v x v. U = 4i + 8k v = 3i + 9j - 6k. (a) u x V (b) V xu

A:

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

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: Solve for u. (u+3)² = 2u²+u+15 If there is more than one solution, separate them with commas.

A: Solution:-

Q: Verify (a × b) × c = (a ∙ c)b − (b ∙ c)a if a = 4i + 2j + k , b = 2i − j + 7k and c = 2i − 2j + 3k

A: Given that a = 4i + 2j + k , b = 2i − j + 7k and c = 2i − 2j + 3k To verify  (a × b) × c = (a ∙ c)b…

Q: iv) (x+ yi)(3i + 2) = (2x – 3y) + (3x + 2y)i %3D

A: The detailed solution is given below Thank you

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

A: We have to prove that LHS=RHS

Q: Compute (2i + k) × (3j + 5k).

A:

Q: V(A - B) = A x (V x B) + B x (V x A) + (A - V)B + (B V)A,

A:

Q: evaluate (1 – 2i) – (-3+ 4i) O V13e-0.983i O 2V13e -0.983i A O 2 13e0.983i O 13/2e0.983i

A:

Q: A rectangular poster has an area of (2x + 3x - 10) square inches. What are the dimensions of the…

A: We can find the dimension of the rectangle as below.

Q: B|a- Find u.v and v xu if u=i+2j-k and v=-2i+2j+2k

A: We have to solve given problem:

Q: If v = 7i + 3j and w = 4i - 5j, find 6v - 3w.

A: Given v=7i+3j and w=4i-5j We have to find 6v-3w. 6v-3w=67i+3j-34i-5j=42i+18j-12i+15j=30i+33j

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: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Solution:Given    v=-i+3j+2k              w=3i-2j-kFind:(a)v×w(b)w×v(c)w×w

Q: Sketch v = (−2, 1), w = (2, 2), v + 2w, v − 2w.

A: Given vector, v = (−2, 1), w = (2, 2)

Q: Determine the conjugate of the product of, (3 – 2i) (4 + 3i)

A: solution:-3-2i4+3i=34+3i-2i4+3i=12+9i-8i-6i2putting i2=-1=12+9i-8i-6-12=12+9i-8i+6=18+i

Q: ..=A+B Ā +B al. B = 2ī + 2j - 2K 3Ā = -i- 3j- k US 1/

A: Given A¯ = -i¯-3j¯-k¯B¯ = 2i¯ +2j¯ -2k¯

Q: x1 – 2x2 – 4x3 = -4 -x1 + 3x2 + 6x3 = 5 -3x1 + 6x2 + 13x3 12 xi = Ex: 42 : x2 = Ex: 42 : X3 = Ex: 42

A: System of non homogenous equation problem....

Q: Given the vectors V and w in the figure below, X 13 근 AREA = 60 units² y

A:

Q: Az = b, where A = (A) 7/6 1/6 (D) [2/3] 1 3 b = 189 11 [Q] X2 Compute projcol(A) (b), the projection…

A: The matrix .The objective is to find the projection of  onto .

Q: t2-3t - 40 2 t + 8t + 15 t +3

A: First factories the given expression than add algebraically.

Q: 8. 2dx 3 3x

A: Given

Q: If u(x) = 4x² — 7 and v(x) = x³ – 9, find u(x) · v(x). . u(x) · v(x) =

A: