Suppose u, v and w are nonzero vectors in 3-space and a is a scalar. Which of the following are true? Select all that apply. DA v x w = 0 whenever v is orthogonal to w В. ||u x v|| = ||u|| ||v|| sin(8) OC. v x w = 0 whenever v is parallel to w OD. u. (v x w) = (u - v) x w OE. (u+ v) x w = u x (v +w) (av) x u = v x (au) F.

Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: Let u, v, w be vectors and k be a scalar. Which of the followings are false? I. u X v= v × u I. и.…

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Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: If u is a vector and a is positive scalar satisfying   au+1,-2,5=0.  To find : a and u.

Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: (a) Prove that if u is orthogonal to both v and w, then u is orthogonal to v + w. (b) Prove that if…

A: Given: (a) If u is orthogonal to both v and w. To prove:  u is orthogonal to v + w. (b) If u is…

Q: A, B, and C are 3 distinct points with non-zero position vectors a, b, and e respectively. a If a x…

A: Given three distinct points are A, B, C. with position vectors a, b, c respectively.…

Q: Let x and y be vectors in the R³. Suppose that x is a scalar product of 2 and the vector y. Prove…

A: x and y are vector in R3, x is scalar or dot product of 2 and y vector,  it means x = 2.y,

Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

A: Here, given that a=-5,2,1,b=-3,-4,3. To find scalars s and t such that: s a+ t b=-7,-18,11 That is:…

Q: If F(x,y,z)=1i+2j+3k, then O1. P=1 Q=2 and R=3 are vectors of F. O II, P=1 Q=2 and R=3 are gradient…

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Q: Suppose u, v and w are nonzero vectors in 3-space and a is a scalar. Which of the following are…

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Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

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Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

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Q: Let u, v, w be vectors and k be a scalar. Which of the followings are false? I. u x v = v x u II. u.…

A: given: u, v and w are vectors and k is a scalar. we have to determine which of the followings are…

Q: Let u, v, w be vectors and k be a scalar. Which of the followings are false? L.uxυ υχu I. и. (ъ х w)…

A: We have to choose the correct answer from the given condition

Q: Let V be the set of vectors shown below. V= x<0, y< a. If u and v are in V, is u + v in V? Why? b.…

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Q: (b) For any arbitrary vectors u, v and w, prove that (u x v) x w = u x (v x w) if and only if (u x…

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Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: If |r (t)| = c (a constant), which of the following is NOT true about the vector function r(t) от ()…

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Q: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  &amp; v = 5a 2 0 are…

Q: If x = (x1,x2)T, y = (y1,y2)T, and z = (z1,z2)T are arbitrary vectors in R2, prove that (a) xTx ≥ 0…

A: The objective is to prove the above expressions.

Q: A vector u for which || u || = 1 is called a(n)_______ vector.

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Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

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Q: True or false 1- The value of v→⋅(v→×w→) is always zero. 2- For any scalar c and any vectorv→, we…

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Q: The vectors v1,V2.Vn in a vector space V are said to be linearly dependent if CV+C2V2+.…

A: By using definition of linearly dependent and independent.

Q: Two vectors u and v in space are if and only if u .v=0

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Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ &amp; v→ Nonzero scalar α v→=αu→

Q: . Prove that for any two vectors d and b in R³, there exist two vectors bí and b such that: T = 6 +…

A: The vectors a→ and b→ lie in the 3 dimesional axes.Any vector is a sume of two vectors.Thus,…

Q: If v is a vector in R", and if k is any scalar, then: (a) ||v|| 20 (h) x = 0 if and only if y = 0

A: Given: v is a vector in ℝn and k is any scalar To show that  a) v≥0 b) v=0 if and only if v=0

Q: (1) Let x and y be the vectors x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z is…

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Q: 3. 2 Find a non-zero vector in R* which is orthogonal to 1 and 2 1

A: Given vectors are 1234, 3121 and 2311. We have to find the non-zero vector in R4 which is orthogonal…

Q: Prove that for any vectors u, v, and w in R2 or R3, we have u ·(v + w) = u · v + u · w.

A: Let u=u1, u2, u3  ,  v=v1, v2, v3  &amp;  w=w1, w2, w3 be the vectors. Now, v+w=v1, v2, v3+w1, w2,…

Q: (1) Let x and y be the vectors -- -- -) x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z…

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Q: Suppose V₁ is a vector of all entries 1 in R" space, which we call "1-vector". What is ||v₁||2 (12…

A: Given: v1 is vector of all entries 1 in ℝn space. To find: v12 for n=16

Q: The dot product ol tWU veciurs Y1 Y2 and y = Yn in R" is defined by a· j = x1yh + x2y2 +... + x„Yn.…

A: Given: x=8-83 We need to find a vector y such that x.y=0. This can be done as follows:

Q: Let W be the set of all vectors of the form t - s Find vectors u and v in R' such that W = span {u,…

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Q: 3. For any vectors U, V and scalars a, b, prove that (a) (aU) x (bV) = ab(U x V)

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Q: Let u, v, w be vectors and k be a scalar. Which of the followings are true? I. u x v = v x u II. u.…

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Q: For any vectors U, V and scalars a, b, prove that (aU) x (6V) = ab(U × V) (a) (b) (aU) - (bV) = ab(U…

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Q: (2) Given the vectors - -- -- --- 1 V1 = V2 = V3 = and w = are there scalars a, b, and c such that…

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Q: Let u, v, w be vectors and k be a scalar. Which of the followings are false? Luxv=υxu II. u. (v × w)…

A: To determine which of the statements are true, we must follow the rule of cross multiplication of…

Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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Q: Two vectors u and v in space are if and only if u .v = 0

A: Condition of dot product.

Q: Let u= 2 and v= 2. Show that among all the scalar multiples cv of the vector v, the projection of u…

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Q: Let {u1,..., un} be an orthonormal set in R". It is a fact that for any vector v E R", there exist…

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Q: Let u, v, w be vectors and k be a scalar. Which of the followings are false I. u x v = v x u Π.u (vx…

A: The formula (I) is false, as cross product of two vectors is not commutative. (II) is correct.

Q: Let W = {[x]∈ R2^ | y > or equal to 0} .             [y] (a) If u and v are vectors in W , is u + v…

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

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Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

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Q: Q1. In each part determine whether the given vectors are orthogonal with respect to the Euclidean…

A: Two vectors u , v are orthogonal if and only if u.v=0 (a) Given u = 2 , 3 , -1 , 0v = (3 , 6 , -2 ,…