Let u = (1,3, 5) and = (-4, 3, –7) be vectors in R³. Find proj, u. Find proju v.

Q: Determine whether or not the given two vectors are parallel.u =〈-3, 1, 4〉, v =〈6, -2, 8〉

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Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

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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: Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

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Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: For the vectors u= (-3,0,4) and v= (1,3, - 3), calculate projyu and scal, u. proj, u = OOD

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Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: Find the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: For the vectors u=−1,4 and v=−4,2​, calculate projvu and scalvu.

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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: Suppose that u, v, and w are vectors such that «u, V> = 6, «v, W> = - 7, cu, w> = 13, ||u||= 1,…

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Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Find the vector v = PQ. %3D P = (2,3,4) Q = (2,5, 10) V =

A: The vector v is given by v=<q1-p1,q2-p2,q3-p3> therefore   if P=(2,3,4) and Q=(2,5,10) then

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

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Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Determine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work…

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Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: Use the given vectors to compute u + v, u − v, and 5u − 3v. u = (5, −2),    v = (7, 6)

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Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: For the vectors u = (- 1,3) and v= (- 4,2), calculate proj,u and scal,,u. proj,u = ( -2,1) scalyu

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Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, −2, 2), ⟨u, v⟩ = u1v1 + 2u2v2 + u3v3

A: u = (1, 1, 1), v = (2, −2, 2), ⟨u, v⟩ = u1v1 + 2u2v2 + u3v3 We need to find the angle θ between the…

Q: The vectors u = (5, −4, 0) and v = (5, -4,0) and v = (−4, −5, 4) are orthogonal. Select one: O True…

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Q: Determine whether or not the given two vectors are parallel.u =〈4, 2, -6〉, v =〈2, -1, 3〉

A: To determine whether or not the given two vectors are parallel.u=4,2,-6 and v=2,-1,3 By definition,…

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: 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: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Suppose that u, v, and w are vectors such that Evaluate the given expression. u-v-2w, 4u+vi= (u, v)…

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Q: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

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Q: Use the vectors u = (4, 4), v = (-7, 2), and w = (4, –1) to find the indicated quantity. (u · v) –…

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Q: For each pair of vectors, calculate projvu and the vector component of u orthogonal to v. (a) u =…

A: Vector components

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: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (17, –18, –1) V

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Q: Consider the vectors u = (-5, -9, 3) and v = (1, -9, 3). Determine u x v. A) (0, 19, 54) B) (0, 18,…

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Q: For the vectors u (1,0, 1) and v (0, 2, 1), u x v = %3D O A. (1, 2, 0) O B. (1, 2, -2) OC. (2, 1, 2)…

A: Given. The vectors u = 1, 0, 1 v = 0, 2, 1 We have to find u×v

Q: u

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Q: Suppose that u, v. and w are vectors such that (u, v) = 2, Evaluate the given expression. (v, w) = -…

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Q: Use the given vectors to compute u + v, u- v, and 3u - 5v. u = (2, -6), v = (4, 5) u + v = u - v =…

A: We will use the usual inner product for the compute the required vectors

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: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: Find the vector z, given that u = (7, 6, 7), v = (2, 2, –1), and w = (4, 0, –4). z -u -v + 2w

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