Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

Q: It is given: ||m| = 4; ||= /3; (m,n)=150°. %3D i. Find the norm of the vector m + 2n. ii. Determine…

A: Given, m→=4n→=3m,n^=150° The angle between the vector m→ and n→ is θ=150°.

Q: a) Given the vectors in M22 . 1 1 2 3 31 22 1 2 21 Show that they are linearly independent. b) Find…

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Q: Consider the following vectors: 17 -2 -2 u = | 2|, v w = and b 3 2 When b is expressed as a linear…

A: Here we solve the system of linear equation .

Q: -5 and 4 4 k are orthogonal. k =

A: We know that if two vectors u & v are orthogonal to each other then the dot product or scalar of…

Q: 4. Find the value of t such that the vectors ~v = h2t + 1,-3,3t - 2i and w = h7,4t +2,2i are…

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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: find all values of the scalar k for which th e two vectors are orthogonal.

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Q: If k is a real number, then the vectors (1, k), (k, 5k + 14) are linearly independent precisely when…

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Q: For which value of a , the vectors î +} – k , î – 2î + 3k and 3î + a ĵ+ 5k are coplanar? -3 O 3 O 4

A: The given three vectors are                                              A→=i^+j^-k^…

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: Given vector U= ⟨1,-1⟩ and V=⟨1,1⟩, find a linear combination of the vectors u and v of the form aU…

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Q: Consider the following vectors: 2 3 u = 3 v = -4 W = 17 2 Express w as a linear combination au+bv.…

A: The given vectors are  u=23-1  , v = 3-42,  w= 017-7

Q: Find the vectors T, N, and B at the given point. r(t) = re) - (2. 20,0). (1, - 3 -1) T = N = B =

A: Here we have to find,  Unit tangent vector T→(t)=? Unit normal vector N→(t)=? Unit Binormal vector…

Q: snip

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Q: Find the value of k for which the vectors 4 and 4 k are orthogonal. k =

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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: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: Find the value(s) of h for which the vectors are linearly dependent. [1 10. 3 11.-5

A: Given vectors are L.D if

Q: Find a value of k such that the given vectors are linearly dependent [ -2 4+ k 4 ,X2 = 2 X1= ,X3 =…

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Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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Q: If k is a real number, then the vectors (1, k), (k, k + 56) are linearly independent precisely when…

A: If k is a real number, then the vectors (1, k), (k, k +56) are linearly independent precisely when k…

Q: Given two vectors t = (1,2, 3) and ở = (1,0, – 1), find (a) t . ở (b) a vector that is orthogonal to…

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Q: Find the value for x such that the following vectors are orthogonal. 3 1 4 -2

A: The dot product of two vectors x, y in Rn is…

Q: The value of k is 5 so that the vectors u= (30, 6) and v = (5, -k) are orthogonal. O True O False

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Q: Find the value of k for which the vectors and 4 -4 are orthogonal. k =

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Q: Find the value(s) of h for which the vectors are linearly dependent. [1 11:-5 -2 6.

A: To find the value of h for which the vectors are linearly dependent.

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: Find the value of c for which the vectors -2 and c-3 in R'are linearly dependent. Select one: 1 2 O…

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Q: Given the vectors v = 4i + 2j +k and w = 3i – 4j + k. Find | 2v – w |

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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: 5 Given that p andr , find in column vector form: 4 p-r ep-2

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Q: 1 1 -1 |1– 5k + k² 1+4k 1– 2k 3 -2 1

A: we can write the given vectors as a linear combination of vectors…

Q: Q1. Construct an orthogonal set of vectors from the following vectors: X1 = k,X2 ,X3 %3D 14]

A: Use the usual inner product in the vectors and Gramm-smidth orthogonalisation process.

Q: Find the value(s) of h for which the vectors are linearly dependent. [1 11.-5 8 h 6.

A: We have to observe the relation between the vectors.

Q: Consider the following vectors á = 2ī+3j and b = -2ī+ 3k and c = −3ī + k

A: topic- projection of one vector on another

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A: Assume that the set 123,  41-2,  ab3 is an orthogonal. This implies that, a, b, 3·1, 2,…

Q: Which of the following vectors are linearly independent? B) [1 2 3] 37 206 S75 R이 기이 46l GaF

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Q: 11 If m = 2i + 3j + 5k & ñ = i + 2j + 2k find the projections of m parallel and perpendicular to n.…

A: If m→=2i+3j+5k & n→=i+2j+2k, then to find the projections of m→ parallel and perpendicular to…

Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

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Q: Find the value(s) of h for which the vectors are linearly dependent. 2 3 4 - 7 h 4

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Q: Find the best approximation to z by vectors of the form c,v1 + C2V2. 2 1 - 5 1 - 1 3 - 3 2 1 1 The…

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Q: Find the value of k for which the vectors -5 -1 4 and -4 k are orthogonal. k =

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Q: Suppose that u = – 2i – 5j and v = - 3i – Compute the given linear combination of these two vectors.…

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Q: If a = 2i – j+k and b = 2j – k, for which value of t are the vectors a + tb and a orthogonal? 6 2 -3

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Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

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

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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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