What can be concluded about non-zero vectors ū, v and w if a) ū ·v = 0 b) ūxi = 0 c) (ū x v) · w= 0

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: Verify the Pythagorean Theorem for the vectors u and v. u = (1, -1), v = (1, 1) Are u and v…

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Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

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Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Let x, y, z be (non-zero) vectors and suppose that z = -3x+ 4y and w = -6x + 8y – 4z. Are the…

A: Solution for 1: Given that  x, y, z be (non-zero) vectors such that z=-3x+4y and w=-6x+8y-4z. Now,…

Q: Prove the stated property of distance between vectors. d(u, v) = d(v, u) for all vectors u and v

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Q: Prove the stated property of distance between vectors.d(u, v) = d(v, u) for all vectors u and v

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Show that span(u, v) = span(u, u + v) for any vectors u and v.

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Q: Find a unit vector u in the direction of v. Verify that ||u|| = 1. v = (-6, 6)

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Q: Find a unit vector orthogonal to both u and v.u = (2, −1, 3) v = (1, 0, −2)

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Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: Find the angle θ between the vectors.u = (−4, 3), v = (0, 5), ⟨u, v⟩ = 3u1v1 + u2v2

A: Now,

Q: 3. Find the projection of u = (2,1,2) onto v = (0,3,4) and the vector component of u orthogonal to…

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Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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Q: Prove the stated property of distance between vectors. d(u, w) &lt;= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

Q: Find a unit vector perpendicular to both u = (2,3, –4) and v = (-1,1,–4). %3D

A: The unit vector perpendicular to u and v is given by: w=±(u×v)|u×v|

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: Find a unit vector orthogonal to both u and v.u = (−4, 3, −2) v = (−1, 1, 0)

A: Given u→=(-4,3,-2)v→=(-1,1,0) unit vector orthogonal to both u and v is gruen by     u→×v→‖u→×v→‖

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

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Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x + y. :Select one…

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Q: 2. The cross product of two vectors u and v is. to u and to v. Thus if both vectors u and v lie in a…

A: Given two vectors u and v

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x+ y. :Select one…

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Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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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: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

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Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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Q: vector that is orthogonal to both u and v. u  =      v  =   <15, −18,

A: Given vector u→=-8,-6,4                    v→=15,-18,-1Now , u→ x v→=i∧j∧k∧-8-6415-18-1u→ x…

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

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: Exercise 4. Is it possible to have nonzero vectors u, v in V with uv = 0? Why or why not? (Here the…

A: Given: 4) V is a subset of vectors in Hamilton's quaternions. To explain: Why or why not there are…

Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Describe all vectors v that are orthogonal to u

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Q: Prove the stated property of distance between vectors.d(u, w) &lt; d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: Find a unit vector that is orthogonal to both u and v.      u = ⟨−8, −6, 4⟩,          v = ⟨10, −12,…

A: Consider the following vectors: u=-8,-6,4v=10,-12,-2 A vector orthogonal to both u and v is the…

Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(-5,-3)

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Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…