8. Determine the dot product of u = [5,-3,1] and v = [2,–2,3]. %3D V%3D

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find (a) ⟨u, v⟩, (b) ||u||, (c) ||v||, and (d) d(u, v) for the given inner product defined on Rn.u =…

A:

Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (1, 1, 1), (5,…

A: Given that, u=(1,1,1) and v=(5,2,5).

Q: (a) a = (2, 6, 0) , b = (4, –1, 1) (b) a =i-j-k, b = }i+j- 4k

A: a) given that  a=<2,6,0> , b=<4,-1,1> a→=2i+6j+0kb→=4i-j+ka→×b→=ijk2604-11…

Q: A) compute x the component of x that is parallel to L and x the component of x that is orthogonal to…

A:

Q: Find the cosine of the angle between the vectors P1(x) = 1+ 2x -x² and p2 (x) = -2-x+ 3x2 with…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the cross product a × b. a = (1, 1, – 1), b = (3, 8, 10) Verify that it is orthogonal to both a…

A:

Q: (3,8, 0) is u x v = %3D So the cross product of u = (1, 0, 1) and v =

A:

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: 8. Determine the dot product of u = [7,-4.1] and v = [3.-2.2].

A: Dot product is also known as the scalar product.

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

Q: Find (u, v), u, v|, and d(u, v) for the given inner product defin u-(-5,4), v = (0,-2), (u, v) = 3u…

A:

Q: Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их

A: Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Q: Find || U || and d(U, V) relative to the standard inner product on M22. 6. #].v=[ -10 15 45 10 U 1…

A:

Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (3, 0, 1), v =…

A:

Q: Find the cross product a ✕ b. a = (7, 0, −2) , b = (0, 6, 0) Verify that it is orthogonal to both a…

A:

Q: Use the indicated entry as the pivot and perform the pivoting. $3 z 0 0 60 o ol 80 1 0 300 0 10 X1…

A:

Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: please help me with this exercise

A: Given,

Q: please help me with this exercise

A: The given vectors are

Q: Find the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b:…

A: Given data:     The first vector is: a=<a1, a2, a3>=<6, 0,-2> The second vector is:…

Q: Calculate the cross product assuming that u × w = = (4, 8, -3) (-u – 4w) × w =

A:

Q: (1 point) If a = i +j+ 3k and b =i+j+2k Compute the cross product a x b. axb 0 i+0 01

A:

Q: Find the cross product a × b. (1, 1, -1), ь %3 (2, 8, 10) a = Verify that it is orthogonal to both a…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find the cross product a × b. a = (2, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

A: We can find each of them by using the besic definition

Q: Find the cross product a X b. a = (4, 5, 0), b = (1, 0, 9) Verify that it is orthogonal to both a…

A:

Q: Calculate the cross product assuming that u x v = (4, 3, 0). v x (u + v)

A:

Q: Compute the component of u along v. u =〈3, 2, 1〉 v =〈1, 0, 1〉

A: Given the vectors are u=<3,2,1> and <1,0,1>.Our Aim is to compute the component of u…

Q: compute the component of u along v. u = (3, 0, 9), v = (1, 2, 2)

A: the given vectors are: u=3,0,9v=1,2,2 we have to compute the component of u along v.

Q: Calculate the cross product assuming that u × v =〈1, 1, 0〉, u × w = 〈0, 3, 1〉, v × w = 〈2, −1, 1〉 v…

A:

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

A:

Q: Calculate the cross product assuming that u X w = (7, 6, 2) (-3u + 4w) × w =

A: We need to find cross product.

Q: Compute the dot product u. V. 02 08 5,V= 0-8 3

A:

Q: 10) Find the cross product a x b and verify that it is orthogonal to both a and b. a =  j + 7k,…

A: Let's find.

Q: Find a lower triangular L and an upper triangular U so that A = LU. %3D 1 2 0 1 2 4 1 4 A = %3D 3 6…

A: Given: A=120124143639 To compute L & U

Q: Calculate the cross product assuming that u x w иxw3D (2, 6, 1)

A: Given vector u x w <2, 6, 1>

Q: 18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k

A:

Q: Calculate the dot product of x = (3, -2, 0, 3) E R and y = (1, 2, 3, 4) ER4.

A: The dot product of two vectors x=(a1,a2,a3,a4)  and  y=(b1,b2,b3,b4)in 4th-dimensional space is: x.y…

Q: What is the Cartesian Product of Z × X × Y, where X = {3,–1}, Y = {m, l, 0} and Z {w,b}.

A:

Q: Calculate the cross product (v + w) × (5u + 4v) assuming that uxv = (1,1,0), uxw= (0, 3, 1), v×w=…

A:

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

A:

Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

A:

Q: Find the cross product a x b. a = (7, 6, -5), b = (2, -1, 1) Verify that it is orthogonal to both a…

A:

Q: Find the cross product a x b. a = (1, 1, -1), b= (2, 8, 10) Verify that it is orthogonal to both a…

A:

Q: Let B= { }],19} be basis for IR. %3D Find [v]g where V= 15

A: Given :                          Basis  B = 3-30, 22-1, 114 and V = 15-93…

Q: The dot product of u = ⟨u1, u2⟩ and v = ⟨v1, v2⟩ is u ∙ v = ________.

A: Dot Product: The vector is u=(u1,u2)v=(v1,v2)u=u1i+u2jv=v1i+v2j