Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−7, −2⟩

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Q: ow that c=3i -2j1+k and d=2j+ 4k are orthogonal.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the length and direction (when defined) of u x v. u = 2 i+ 2j- k, v = -i+ k

A: As per our guidelines we are supposed to answer only one question and rest of the questions are…

Q: Find w such that 2u + v- 3w = 0. %3D u = (0, 5, 7, 2), v = (-3, 4, -8, 1) W =

A: vector

Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0

A: we know that  uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…

Q: Let u = (1,2,3) and v = (2a,2a,a^2) Which of the following values of a ensures thatu and v are…

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Q: Let u= (1,1,−2) and v= (a,−1,2). For what values of a are u and v orthogonal?

A: Two vectors are said to be orthogonal to each other if their dot product is zero. we are given u=…

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v = {8, 1) a = b =

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Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: Let overline u =(2.2-4) and overline v =(a,1-1) . For what values of 'a' are u and v orthogonal?

A: Let overline u =(2.2-4) and overline v =(a,1-1) . For what values of 'a' are u and v orthogonal?

Q: Let V = [3, – 1, – 4] and W = [0, 2, k]. Find a real number k so that V and W will be orthogonal. k…

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

Q: Find solutions of the linear PDE u, + yu, =0 , given that u(0, y)= y'. ди(х, у) ди(х, у) Notation is…

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Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: let V be the Euclidean space R3 with the standard inner product.

A: Given:          u = 11-2  and  v = a-12 To find :             The values of a, for which u and v…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). %3D %3D = (0, 6) V = a b…

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Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

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Q: Let v = Does {v1, V2, V3} span R*? Why or why not?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Consider the set S = {p, q, r}, where p=1+x, q= x-x² and r= 1+ 2x². Show that the set S is linearly…

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Q: Given v = (8, –3) and w = (12, -4), find vector projection of v onto w.

A: Solution; Consider the given vectors :  v = 8, -3 and w = 12, -4 Now, vector projection of v onto w…

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨1, −3⟩

A: Given: v=au+bw; u=1,2,v=1,-3,w=1,-1 for finding value of a and b, we put value of u,v,w in given…

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−1, 8⟩

A: Given that v = au + bw. Substitute u =<1, 2> and w= <1, -1> in v.…

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (1,…

A: Given u=1,2 and w=1,-1 , v=1,-4we write v is a linear combination of u and w if possible .

Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

Q: Let f (x, y) = x² – y² . Find all all points (æ, y) such that Vf (x, y) = ±(1, 1).

A: givenf(x, y) =x2-y2∇f(x, y) =±(1, 1)

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (0,…

A: Here u = (1, 2), w = (1, -1) and v = (0, 3) Since v is a linear combination of u and w So consider v…

Q: Consider the vestun . il 1:= V2: V3: and u where a E R. (a) For which values of a is the span(v1,…

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Q: Let u = (1,2,3) and v = (2a,2a,a2) Which of the following values of a ensures that u and v are…

A:

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨4, 5⟩

A: we have to find a and b such that v=au+bw where u=1,2 and w=1,-1 and v=4,5. the given vectors are:…

Q: Find the length and direction (when defined) of u xv and vxu. u= - 12i + 8j – 20k, v = - 3i + 2j -…

A: To find the length and direction of u→×v→, first find the value of u→×v→ by cross product. The given…

Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

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Q: Let u = (k, 2 − k, −1), v = (2k, k, 3). Find k such that u and v are orthogonal.

A: Let u = (k, 2 − k, −1), v = (2k, k, 3)

Q: Suppose v1,..., Vk are linearly independent vectors in R" (1 <k < n). Then the set Xk =…

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Q: Let u = (2, 1, – 1) - (-4, α + β 2) w- (α, 0, β ) Find the values of a and ß such that u is parallel…

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Q: Find (u, v) for (u, v) = 2u,v, +3u, v, +u,v, defined in R, where u (9,0,-3) and v (8, 2,17). A. (u,…

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Q: Let X = y = z = and Find r and s so that (а) z %3D 2х, (b) u = y, (с) z+ u %3D х.

A: x=12,  y=-3  4,  z=r4  &amp;  u=-2  s a). z=2x⇒r4=212⇒r4=24⇒r=2

Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: Given that v = (2,3, 4), vị = (1,0,1), v2 = (0,-1, 1), vz = (-1,-1,1). Express v as a linear…

A: Given, v=2,3,4, v1=1,0,1, v2=0,-1,1, v3=-1,-1,1

Q: Let a and b be orthogonal such that |ã| = 2 and b = 3. %3D Find (b x a) x ả and |(b × å) × |

A: Given a→=2 and b→=3 We have to find b→×a→×a→   and b→×a→×a→

Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v = (9, 3) a = b =

A: This question is based on vector form.

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

A: It is given that,  v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

Q: In writing v as a linear combination of u ,,u, &u, ( if possible) given: y = (3,0, – 6) , u,= (1, –…

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v = (0, 12) a =

A: We can find the value of a and b as below.

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v= (0, 24) a = %3D

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v (0, 24) %3D a =…

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Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). = (5, 4) a =

A: It is vector problem.

Q: Let u= (2, 1, –1) v- -4,3α + β, 2) w- (α, 0, 2β) Find the values of a and B such that u is parallel…

A: Given, u=2,1,-1v=-4,3α+β,2w=α,0,2β