23. Are the vectors u = <6,-10 > and v = <-5,-3 > orthogonal? Explain.

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

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: What is meant by the term translation in vectors?

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Q: Verify the Pythagorean Theorem for the vectors u and v.u = (3, −2), v = (4, 6)

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Q: ind a unit vector orthogonal to bothu and v. u = (-8, 7, -2) v = (-1, 1, 0)

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Q: Explain why u + v • w _is not defined, where u, v, and w are nonzero vectors.

A: Given 3 non zero vectors : u , v and w. We need to explain why  u + v . w is not defined.

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

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: Can three vectors in the xy plane, R^2, have u.v<0, v.w<0, w.u<0

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Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: Are vectors v = ⟨ − 2 , − 3 ⟩ and u = ⟨ 6 , − 4 ⟩ orthogonal? Yes or No:

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Q: 2 Find the angle between two vectors Ā - Hax-Gay -89z B-Gax + 10ay + Saz

A: Angle between two vectors A⇀ and B⇀ is θ=cos-1A⇀·B⇀A⇀B⇀

Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

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

A: Solutions

Q: help me is for my test of today -II- Find two vectors in opposite dimensions that are orthogonal to…

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Q: What us the midpoint between vectors: A = [3,4,5] B = [1,-1,1]

A: To find the midpoint of the vectors A = [3,4,5] and B = [1,-1,1] We have, x1=3, y1=4, z1=5, x2=1,…

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: Compute the distance between the vectors u = and v = 315

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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: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

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Q: Two linearly independent vectors in R3 span R2, is that true

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

A: Consider a parallelogram formed by the vectors u and v. Find the area of the parallelogram. Area of…

Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

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Q: Explain why u + v ∙ w is not defined, where u, v, and w are nonzero vectors.

A: Let us assume that u,v, and w are nonzero vectors.  The dot product of the vector of the scalar…

Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

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

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Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: 9. Which is traveling faster, a car whose velocity vector is 217 +35j or a car whose velocity vector…

A: We are authorised to solve only one question, please repost remaining questions Magnitude of vector

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: 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: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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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: tind a non-zero vector perpendıcular to the vectar u. Find the length of the vector R-

A: Consider two vector u→=ai→+bj→ and v→=ci→+dj→ if the two vector is perpendicular then the angle…

Q: Find the angle θ between the vectors.u = (3, 4), v = (5, −12), ⟨u, v⟩ = u ∙ v

A: Given vector: Formula used : By dot product equation:

Q: Describe all vectors v that are orthogonal to u

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(15,0)

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Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: Determine whether the vector U = 2 is a linear combination of the vectors Xi = 2 X2 = and X ? Give…

A: Let  U→=aX1→+bX2→+cX3→  Where, a,b and c are scalar. Then,…

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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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: s opposite or equal vectors?

A: Consider the given information as Are parallel vectors always opposite or equal vectors

Q: a) tor which values on a are the vectors 87 2 -- a linearln independent?

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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…