1. Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v

Q: Let u and v be two non-zero vectors in R". Which of the following options can we conclude are equal…

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Q: 10. Given two vectors u = [6,2] and v=[-2,1], determine the projection of u on v.

A: #10

Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩.   u − v + w − 2z =…

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Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: Suppose U and W are vectors in R" then ||U +W|| - ||U|| + || W|| if the angle between U&W is equal…

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Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: = 2. Are the vectors V = (2, — 4, 1) and w Show work and briefly explain. (3, 2, 2) orthogonal? 3.…

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Q: Suppose that u, v, and w are vectors such that «u, V> = 6, (v, w> = - 7, ku, w> = 13, lu||= 1,…

A: The axioms of vector operations are as follows: <u+v, v+w>= <u,v+w>+<v,v+w> <u,…

Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Let (a, b, c) and (u, v, w) be two vectors, and suppose that a, b, c, u, v, w > 1. What can we…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: .b,č are three vectors such that a + b+ e = 0, lal = 5.6 = 3. = 8 then ä.b+ ans. -49 48 1/6

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Q: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

Q: What is the angle measure between the vectors u = (-5, 8) and v = (3, 9)?

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Q: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: Suppose that u, v, and w are vectors such that cu, V) = 3, cv, w> = – 4, cu, wɔ = 7, ||u||= 1 ||v||=…

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Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

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Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

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Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

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Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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Q: 1. Given the following vectors: u=(1, 2, -4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v

A: Given: u=(1,2-4) v=(2,3,5) To find:  (a) u.v (b) u.u (c) (u.v)v

Q: Compute (m +n)´ if m and n are two unit vectors and the angle between them 30°.

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Q: Consider the following vectors. u = (5, 0), V v = (1, 1) Find the lengths of u, v, and u + v. ||u||…

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Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

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Q: Given the vectors u = (2,1,1,1) and v = (3,2, −1,2), find the value(s) of t such that I.  v . (u +…

A: Given vectors are u=2,1,1,1 and v=3,2,-1,2. To find value of t such that v.u+tv=16. Solution:…

Q: (a) Consider two vectors u = 3 and v = 5 in R4, Show that 5 7 7 i) u.v = v.u ii) d(u, v) > 0 [-31

A: Two vectors u and v is given in R4, and the vector is given as:

Q: Suppose we know that u · v = u · w. Does it follow that v = w? If it does, give a proof that is…

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: b) Find the angle (0) between vectors between s = [1, –5, 4] and t = [3,3, 3].

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Q: 7. Let u and v be two vectors for which ||u||² + ||v||² = ||u + v||² From this information alone,…

A: Given that u2+||v||2=||u+v||2 consider the right hand side of the given equation. ||u+v||2=u+v.u+v

Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: given the vectors from R3 v, = (2 0 3), v2= ( -1 3 0), v3=(2 4 –1) %3D (-5 0 3) belongs to span{v,,…

A: Given vectors are v1→=2,0,3, v2→=-1,3,0, v3→=2,4,-1. To determine: u→=-5,0,3 belongs to span v1→,…

Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

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Q: 2. The area of the triangle whose adjacent sides are the vectors u and v is a) Ju · v| c) |u x v|…

A: It is known that, the area of the triangle whose adjacent sides are the vectors A and B is 12A×B.

Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: 2 3 Given the following three vectors u = 10], v = -5 and w = [-2. ..

A: Formula: Angle between the vectors u and v is given by, θ=cos-1u·vuv Given: u=2100, v=0-58 and…

Q: Find the angle between the vectors u and v if u (2,3,5) and v = : (1,–4,3) in (Ctrl) ►

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Q: Since A, B and C vectors are perpendicular to each other, A, B, C, =? A -6) â, 1 (8) â, + A‚⸠B 19)…

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Q: If u = (1,-3,2) and v = (-2,3,4). Find the distance between the vectors d(u, v) and d(v, u).

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Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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Q: Show that for any two vectors u and v: = |

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Q: Under what conditions are the following true for vectors u and v in IR2 or IR3? (a) ||u + v|| =…

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