Consider the following 3 vectors. v1=[25,−13], v2=[11,−11] and v3=[−17,25]. Take them pairwise, you will get 3 pairs. Now check for linear independence for each pair separately. Which pairs are linearly independent and which are dependent?

Q: If å = v2i +j - k, what is the vector whose alignment a is in the opposite direction and its size…

A: Given a→=2i+j−k We have to find the vector whose alignment a→ is in the opposite direction and its…

Q: For the pair of vectors, find U + V, U-V, and 3U - 4V U = (4,1) V =(-6,3

A: Given that  U = (4,1) V =(-6,3) To find U + V, U-V, and 3U - 4V

Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that r1+r2+r3 is equally…

A: GIVEN: r1 , r2 , r3 are three parallel vectors

Q: Write the following vector as a linear combination of the unit vectors i and j. (-4,Radical 2)

A: We need to the following vector as a linear combination of the unit vectors i and j

Q: For the following pair of vectors, find U · V. U = 6i + 7j, V = 7i + 6j

A: This question is based on Dot product.

Q: The vectors and are Select one: a. Linearly independent b. Linearly dependent

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Q: For what value of t, if any, is the vector (4t, -1) parallel to the vector (4, -1) ?

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Q: If v=3w then the two vectors v and w are ................

A: Given :                    If v = 3w, then the two vectors  v and w are ____________

Q: For the pair of vectors, find U + V, U − V, and 2U − 3V U = 9, 5, V = 9, −5 U+V= U-V= 2U-3V=

A: We know that for two vectors a→=a1,a2 and b→=b1,b2, a→+b→=a1+b1,a2+b2         ⋯⋯1a→-b→=a1-b1,a2-b2…

Q: Find the positive value for which the vector r(t) = (3t, 10t², 7t² – 2) is perpendicular to r'(t).

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Q: Consider the following 3 vectors. v1=[25−13], v2=[11−11] and v3=[−1725]. Take them pairwise, you…

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Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: photo attached

A: Given vectors are

Q: For the following pair of vectors, find U · v. U = -11i + 5j, V = 9i – 3j

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Q: Perform the following operations on the vectors u = (1, 3) and v = -3,4, a. |v| b. u· v c. Angle…

A: We can answer all the three questions as below.

Q: Let a and y 6 Find the vectors v = 5x, u = x + ÿ, and w 5a + %3D || ||

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Q: For what value of t , if any, is the vector (4t, -1) parallel to the vector (4, -1) ?

A: Given :4t,-1 and 4,-1

Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: Find the cross product of the vectors ä = and b = .

A:

Q: For each of the following vectors b€ Rª, decide whether b is a inear combination of V1, V2, and v3.…

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Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

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Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: For the pair of vectors, find U•V. U = 4i+j V= 3i-j O 8 O 12 O 13 O 1 O 7

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Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: For the following pair of vectors, find U · V. U = 6i + 2j, V = −6i + 2j

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Q: For two vectors a and b, V

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Q: For the following pair of vectors, find U · V. U = i + j, V = i − j

A: We need to find scalar product of two vectors

Q: Find the sum of the given vectors; + B Å = 440 N Z 236°, B= 580 N Z 162° Draw and label a diagram…

A: Obtain the graph of vectors as follows: The third arrow is the resultant vector.

Q: photo attached

A: Given,

Q: Find the following for the vectors

A: Given that: v=-9i+ju=-5i+7j     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Given v=[2,-9] and w = [7,-8], what is 2w-v written as a linear combination of unit vectors?  please…

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Q: Consider the following vectors: -4 3 -4 -2 1 |, w = -2 , and b = -2 v 1 4 When b is expressed as a…

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Q: For the given vectors a and b, find the cross product a x b. = (4, 0, –3), b = (2, 3, 0) a x b =

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Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: Choose the linearly dependent vectors in R'. Select one: а. O b. O d. -2

A: The solution is given below

Q: For the following pair of vectors, find U · V. U = −7i, V = 9j

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Q: For the pair of vectors, find U + V, U – V, and 3U – 4V. U = (3, 1), V = (-6, 2) U + V = U - v = 3U…

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Q: Q3. Find the cross product of the vectors and .

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Q: For the following pair of vectors, find U · V. U = −2i, V = 9j

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Q: Perform the following operations on the vectors ū = (5, –2, 1), v = (-1, –2,0), and (3, 3, –4). w =…

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Q: Consider the following vectors: 2 -2 and b -3 u , V 4 When b is expressed as a linear combination…

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Q: For the pair of vectors U = , V = , find U + V, U - V, and 3U - 4v. U + V =

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Q: For this question, define the vectors v and w .

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Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

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Q: For the non-zero vectors A and B to be perpendicular to each other, the necessary and sufficient…

A: Given, For the non-zero vectors A and B to be perpendicular to each other, the necessary and…

Q: photo attached

A: Given:U = <3, 3>V = <3, –3>