(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

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: In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to…

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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: C A

A: We use Triangle law

Q: find the value of k for which the vectors u and v are orthogonal.  u = 2i - kj v = 3i + 2j

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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: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

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

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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…

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

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

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Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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Q: In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to…

A: V=v1+v2  (Given)when two vector v1 & w are parellelthen the angle between v1 &w is 0° or…

Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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

A: Angle between two vectors, θ=cos-1u→.v→|u→| |v|→ a)  u→.v→=2i+j.i+2j-k       =2+2 u→.v→=4 |u→|=22+12…

Q: Find a unit vector in the direction of vector (v= ai + bj ) and orthogonal to the vector ( u= 3i -…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. 1 Find the unit vector…

A: Given, X = -i + 3j  and Y = 4i -2j + 2k

Q: What are the possible angles θ between two unit vectors e and f if ||e × f|| = 1/2 ?

A: The cross product of two vectors can be found by the formula a→×b→=a→b→sinθ The magnitude of the…

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: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

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: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: 4. Using the vectors: ü=[2,-1,3], v=[4,5,-2], w=[1,-1,7], calculate: a) b) ux v c) ū+ v +2w

A: Here we have to perform the vector operation

Q: Let u, v be two vectors in IR® satisfying ||u|| = V5 and ||v|| = v2 and u. v = -2. %3D %3D Then (u –…

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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: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

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: Use two arbitrary 2-dimensional vectors to verify: If vectors u and v are orthogonal, then ||u||² +…

A: Use the following definitions, to obtain the solution. If a and b are orthogonal vectors, then…

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

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: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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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: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

A: Let u and v be tthe vectors in 3-spaceThen by Lagrange's identity,we haveu×v2 =u2.v2-(u.v)2…

Q: 9. Find two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: A vector perpendicular to both of the given vectors can be found out by finding the cross product of…

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: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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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: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

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Q: (a) (a) Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k а. -

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Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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

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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…