7. and V -8 are orthogonal. 15 The vectors u = %3D L-7 True

Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given: Two nonzero vectors v and w, v can be decomposed into two vectors, one parallel to w and the…

Q: For what value of k are the vectors u = Select one alternative: Ok = -2 k = -1 Ok=2 Ok = 1 (1,-1,-1)…

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Q: التاريخ 5.1 1 1 If the vector [42] An with the straight Piecel the end point?

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Q: find all vectors v⃗  in 2 dimensions having ||v⃗ ||=41 where the j⃗ -component of v⃗  is 9j⃗ .

A: Our objective is to find all the vectors v having ||v||=41 and the j-th component 9j.

Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

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Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: (e) 5. Compute the angle between the vectors [1, –1,0, 1] and [0, 1,0, 2]. 6. Compute the…

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Q: 12 2 Determine if the pair of vectors v₁ = 3 V₂ = =-3 are orthogonal. -5 3

A: We have to find whether the given two vectors are orthogonal or not?

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: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  & v = 5a 2 0 are…

Q: If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w?

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: 2) Show that if u and v are orthogonal unit vectors in R*, then. a) -4=7 b) The vectors a+v and…

A: The set of vectors u1,u2,…,uk of ℝn is said to be orthogonal unit vectors of ℝn if the inner product…

Q: -36 4 3 Express the vector v = as a linear combination of x ar -34 x+ y. %3D ||

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Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

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Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

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Q: 9. V =|-1 Write the vector as the linear combination of the basis vectors 3 4 and u, =|- 3 u, = 2…

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Q: Г 13 and vz = 14 are linearly independent. Determine whether the vectors v 14

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Q: Find two vectors ?⎯⎯⎯1v¯1 and ?⎯⎯⎯2v¯2 whose sum is ⟨2,−5,3⟩⟨2,−5,3⟩, where ?⎯⎯⎯1v¯1 is parallel to…

A: We have to find v1 and V2 vector.

Q: 16. A vector perpendicular to both 21 + 21 - k and -î + 2k is: A. 31 + 4j – 2k B. 31 – 4j – 2k C. 2î…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

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Q: Q2/ If Vi - 5i-j +k V: -j-5k V3--15i + 3j - 3k Three vectors in space. Find if any of V1, V2, and V3…

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Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: 6. We have two vectors: a =) and b= 8 What is the resultant of -a plus b? (

A: Given:     To find: -a + b

Q: 7 7 The vectors v = 3 and w = 6. -23 -32 span a plane in R. If the equation of this plane is ax + by…

A: System of linear equations

Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

Q: -4] is linear Question 2: For what value of "a" the vector v = 5 -4 and v3 = combination of the…

A: Givenv=-43a and v1=1-1-2 , v2=5-4-7 and v3=-310To find value of a such that v is linear combination…

Q: 8. ... The value(s) of h which makes the vectors linearly dependent is(are) because this will cause…

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Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

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Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

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Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: 4 The vectors v = 3 and w = span a plane in R³. -28 -25 If the equation of this plane is ax + by + z…

A: Given: v=53-28 and w=45-25 spans a plane in ℝ3. To find: a and b, where the equation of plane is…

Q: - 3 7 1 h of h which makes the vectors linearly depe ma to separate answers as needed.)

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Q: 2 and v2 = 3 be Work Problem 2 : Let vj = two vectors in R?. (a) i Determine whether v = belongs to…

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Q: -4 If possible, express w as a linear combination of the vectors v1, v2 and v3. Otherwise, enter…

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Q: 9. (a) are perpendicular to each other. Determine the algebraic condition such that the vectors č=…

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Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: га- Find an equation that describes all values of a, b, and c for which the vector w = |b| is NOT a…

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Q: 3.10 Rotate the vectors 2 x1 := 3 [4] x2 := by 30°.

A: As we know that, the rotation matrix when the vector rotates about the z-axis in the…

Q: Hey, please reaply as soon as posible Consider the vectors v and w such that v = (8,0, -8) and w =…

A: Topic = Vectors correct option = b

Q: 3 The vectors u = -4 and v = -12 are linearly independent. 6.

A: Given vectors : u=3-42 and v=9-126 . Therefore,  we will test these two vectors to find whether 'a'…

Q: 4.14. Determine whether vectors u and v are orthogonal, parallel, or neither for u =i and v = -2i+…

A: You need to verify by using orthogonal and parallel test of two vectors using their dot product.

Q: 7 For what value of k are the vectors u Select one alternative: Ok=-1 Ok=-2 Ok=1 Ok=2 (1,-1,-1) and…

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Q: 4. For which value of k the vector u = -2 is a linear combination of the vectors k 3 3 and v2 = of…

A: Given: To find the value of k such that vector u=1-2k is a linear combination of vectors v1=30-2 and…

Q: 1. a. If 37-2ỷ = ở and 5x - 33 = b, express the vectors and y in terms of a and b. %3D %3D

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Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0,…

Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

Q: 1. If vectors u (3, 3), v-(13.-7), and 2w +3u-v 2. When is it true that u+ v=v+u?

A: The symmetric property states that for all real numbers x and y, if x=y, then y = x SO,  u+v =v + u

Q: 4. For which value of k the vector u = -2 is a linear combination of the vectors 3 3 V1 = 0 and vz =…

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