1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal to both a and b.

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Find the cross product a × b. a = (9, 0, -4), b = (0, 8, 0) Verify that it is orthogonal to both a…

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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: Let →a=⟨3,1⟩ and →b=⟨1,0⟩. Find the projection of →b onto →a. proj→a →b=

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Q: Find the cross product u x 7 where u = 51 -3j+k and = (-1, -3,2). uxv=

A: To find the cross product u→×v→ where u→=5i-3j+k and v→=-1, -3, 2.

Q: Calculate the cross product assuming that u x w = (-8, -1, -5) (5u + 3w) x w =

A: Solution

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

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Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: be the bases of V, W and U respectively. If t: V→ W, s : W→U are linear transfor-

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Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

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Q: Draw v = [ 4/1 ] and w = [ -2/2 ] and v+w and v-w in a single xy plane.

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Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

A: We can make it easier for you

Q: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

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

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Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

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: 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: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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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

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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…

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Q: Calculate the cross product assuming that u x w = (-3, 6, 6) (4u - 4w) × w = |

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Q: Let u=-3i+3j+2k and v=i+j+3k and find u . v, that is, the cross product of u and v

A: Let  u→ and v→ be the two vectors .   i.e, u→=u1i^ +u2j^+u3k^  and  v→=v1i^+v2j^ +v3k^ Dot product…

Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: Calculate the cross product assuming that u x w = (-7, 1, -6) (2u + 4w) x w = = (

A: To calculate the cross product of 2u+4w×w, assuming that u×w=-7, 1, -6.

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

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

A: We need to find cross product.

Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: In the xy plane mark all nine of these linear combinations: c[2/1]+d[0/1] with c=0, 1 , 2 and d=0, 1…

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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 the cross product a × b. a-i-j-k, b-tj+* Verify that it is orthogonal to both a and b. (a x b)…

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Q: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

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Q: (B) If A = x³ y z° i- 3 x³y*zj+2 x y k , find curl of A.

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Q: Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the…

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Q: Suppose T: R³ → R² is a linear map and that u and v are particular vectors in R. If T(u) = (2, –3)…

A: Given query is to find the indicated vector.

Q: Let, T: R' → R';T(x, y,z) = (x+ y+ z,2y + z,2y +3z) Find the dimension of KerT and ImT

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

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Q: Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis,…

A: Let O is the initial point (0, 0, 0) and the vector OP, OQ and OR vector can be represented as:

Q: Calculate the cross product assuming that u x w = (-1, -8, -2) %3D (5u + 3w) x w = (

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Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

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

A: Given u × w = -2, -3, -2

Q: Find the cross product a x b. a = j + 6k, b = 31 - j + 2k Verify that it is orthogonal to both a and…

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Q: Prove the following property of the cross product: u X kv = k(u X v)

A: Let u=u1 i+u2 j+u3 k  &  v=v1 i+v2 j+v3 k. Then, kv=kv1 i+kv2 j+kv3 k Now,…

Q: Find the cross product a x b. a = (t, 2, 1/t). b = (r?, r², 1) Verify that it is orthogonal to both…

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

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