In Exercises 1-8, find a. v•u, v]. Ju| b. the cosine of the angle between v and u c. the scalar component of u in the direction of v d. the vector proj, u. 1. v = 2i – 4j + V5k, u = -2i + 4j – V5k

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Q: In Exercises 15-18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

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Q: C A

A: We use Triangle law

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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A: We have given two vectors A→=Axi^+Ayj^  and  B→=Bxi^+Byj^ i^×i^=j^×j^=0i^×j^=k^, j^×i^=-k^   Find…

Q: 3. Find the angles between the vectors: u = 2i + j, u = 2i – 2j + k, v = 3i + 4k a. v = i + 2j – k…

A: a.)u=2i+j , v=i+2j-klet θ be the angle between the…

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Q: Consider (u, v) = 0 for any vectors u, v e R4. Is this an inner product? Explain why or why not. %3D

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Q: In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two…

A: "Since you have asked multiple questions, we will solve the first (20) question for you. If you want…

Q: In Exercises 53-56, let u = -2i + 3j, v = 6i – j, w = -3i. Find each specified vector or scalar. 53.…

A: 53). Given vectors are u=-2i+3j, v=6i-j, w=-3i. To find: 4u-2v-w Solution: We know that scalar…

Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

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Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

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: In Exercises 17 and 18, find |v| , |u| , v .u, u. v, v * u, u * v, |v * u| , the angle between v and…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: In Exercises 1–2, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar…

A: given

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Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

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

Q: Triangles in Space

A: Area of triangle formed by P,Q,R is given by  Area=PQ ⇀×PR⇀2 UNIT VECTOR is given by  unit vector=PQ…

Q: In Exercises 1-8, find a. v•u, |v], |u| b. the cosine of the angle between v and u c. the scalar…

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Q: Find the unit vector u in the di rection of the vector v=2(2, 1, 2).

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Q: Find the angles between the vectors in Exercises 9–12 to the nearest hundredth of a radian. 9. u =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Dot Product and Projections in Exercises 1–8, find

A: 1. Given v=2i-4j+5k, u=-2i+4j-5k (a) To find v·u. v·u=2i-4j+5k·-2i+4j-5k=2·-2+-4·4+5·-5=-4-16-5=-25…

Q: In Exercises 1 - 10, use the given pair of vectors i and w to find the following quantities. State…

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Q: In Exercises 15–18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

A: We'll answer the first question since the exact one wasn't specified . Please submit a new question…

Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

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

Q: In Exercise 24, find the angle θ between the vectors (a) in radians and (b) in degrees. 24. u = ⟨1,…

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Q: 1. Given three vectors u =(1,–3,0), v=(2,1,–1) and w=(0,2,3). Determine: a. Bu + 4v – Sw]. b. Cosine…

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Q: Find a unit vector orthogonal to both u and v. u = 3i – 5j + 2k -k + 10 - V =

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Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

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A: v=4(2,1,2)v=(4*2,4*1,4*2)v=(8,4,8)Magnitude of vector|v|=(8)2+(4)2+(8)2=64+16+64=144=12unit vector u…

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Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: In Exercises 1–3, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: In Exercises 9–14, sketch the coordinate axes and then include the vectors u, v, and u * v as…

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Q: In Exercises 1-8, find a. v.u, v], |u| b. the cosine of the angle between v and u c. the scalar…

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

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