Compute the corresponding distance and angle between B 1 and 3 for the inner products below: (a) (x, y) = xTy; [2 (b) (x, y) = x¹ Ay where A = 1 1 3 ܗ ܘ -1 0-1 2

Q: Find the cross product a x b. a = 5j 6k, b = −i + 2j + k Verify that it is orthogonal to both a and…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are

Q: Let ((u,u2,u3),(V1,V2,V3))=2u,Vị+3u2V2+U3V3 be an inner product on R3. Determine the angle in…

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Q: Given d₁ = [2 11³ and A = [21]. find a vector d₂ = [3 a] that is conjugate with L2 respect to d₁.

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Q: In linear algebra, if a vector is in the range of a matrix A, then it is also in the null space of…

A: The given statement is False.

Q: B: 1. Find (1+ i)* 2. Find the area between the vectors A = 2i – 2j + k , B = 3i + 4k

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Q: Please solve part b and d correctly and explain as well

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Q: For the z-coordinate of the north pole at N(11,9,12), how did you guys get 12?

A: Your question is why maximum value of z is 12?  I show this in two ways. Geometrically Analytically

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

A: Given v=3i+j+3k, w=i-k

Q: Given that F = xz i − 2yz j + x2yz k. Find the followings at (1, 1, 3): (a) div F.  (b) curl F.  (c)…

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Q: Q.2: Find u x v, where a: u = (1,–3,4) & v = (3,4, 7), ats b: и %3D (1,2,3) &v %3D (1,5, 2).

A: Given: a u=1, -3, 4 and v=3, 4, 7b u=1, 2, 3 and v=1, 5, 2 To Find: u×v=?

Q: If V = (3x + 2z²)i + j- (z – 7x)k then V. V at the point. (1, 1, 1) is ||

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Q: The pt. (x,y) is at a distance 5 from (0,-3)

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Q: - - Find the cross product (-2i - j + k) × (3i − j − k). Answer:

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Q: Find the value of β for which w =〈−2, β〉 is parallel to v =〈4, −3〉.

A: Two vectors are parallel if the angle between them is 0 or π. That is, the vectors are pointing in…

Q: Let à x b = -38 i +6 j 20 k Where a = -2 i + 4 j + 5 k and b = mi + 6 j − 2 k, ɓ Calculate m, là b,…

A: Basic formulas from vectors will be used.

Q: Find the coefficient of w2r?y'z? in (2w-z+3y- 2z+2)°.

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Q: Find J(u, v) if x = u + v, y = 2v.

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Q: et F = t+3 2i-fj+3t°k and G = e'i – 3f j+ e²* & %3D

A: Given are two vector functions F=t+3ti-t2j+3t3k and G=eti-3t3j+e2tk.

Q: Assume w = ts³, 4ts) and (x,y) = 6xy of (х.у) - 4х Find as when t = s = 1 %3D

A: Given: From the given expression it is clear that 'f' is a function of 'x' and 'y', and 'x' and 'y'…

Q: 1. The General Social Survey asked a sample of adults how many siblings (brothers and sisters) they…

A: Since you have posted a question with multiple with sub-parts, we will solve first 3 sub-parts for…

Q: Let --) - -() u = |3 and v = 2 5 where y E R. Then the value of y such that u and v are orthogonal…

A: Given that, u=23y and v=-125y∈ℝThe value of y such that u and v are orthogonal is calculated as…

Q: Let a(t) = (– 5, 5, – 2)t + (2, 4, 6) and b(u) 3 (- 3,0, - 4)и + ( - 2, — 8, — 5). Find the acute…

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Q: The symmetric equations for the line passing through (-3,–4, -5) and parallel to the vector (1,7,–…

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Q: Find u x v. u = j + 3k, v = 7i - k Show that u x v is orthogonal to both u and v. (u x v) · u = (u x…

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Q: Let y = [+] and x = 4 a. d(y+x, w) = 1: b. d(y + x, w) = √2: c. d(y+w, x) = 1: d. d(x+w, y) = 1:…

A: Let  and .Find a column vector  such thata. b. c. d.

Q: If v = 3i - 6j and w = i + j, find (v . w)w.

A: Given:          v=3i-6jw=i+j Using the component formula for the dot product of two-dimensional…

Q: How does the cross product i x ì relate to the vectors ở and i geometrically? Use this to compute d…

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Q: Consider the following. 3D(6,-1,0) v = (-2, 3, 0) u = %3D Find u x v. Determine if uxvis orthogonal…

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Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…