1. Given vectors B = (2,–3),C=(6,9) in R² . Examine if they are linearly independent. 2. Given vectors X =(2,-3),W =(6,-9) in R°. Examine if they are linearly independent. 3. Given vectors A= (2,-3,1), B = (6,9,–1) in R’. Examine if they are linearly independent. 4. Given vectors A=(2,-3,1), B = (6,9,–1),C =(0,9,1) in R’. Examine if they are linearly independent. 5. Find constant k so that vectors B= (2,3),C =(3,k) in R² are linearly dependent.

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: 9. Find the dot product of the following pairs of vectors. a. u= (1, 3), v = (5,-2) b. = (9,-4), v =…

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Q: For the following three vectors, what is 2. Ć ·(3 Á × B )? В = 3.00î + 3.00ĵ – 4.00k B = - 3.00î +…

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Q: 1. Three vectors are given by: å = 2î – 3ĵ + 5k, b = -2î + 7j – k and č = lî + 2j – 4k. axb Find a,…

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Q: What value of a will make the vectors (-2, x, 1) and (2, –1, 1) orthogonal? Select one: O a. 3 O b.…

A: For orthogonal, dot product of two vectors are zero.

Q: =3. Let a = [2₁1,-1], 5o = [4₁-5, 3] and C-[-1,-2,5]. compute ax (b + c). Show full steps.

A: We have to solve given Questions.

Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: Find the cross product of the vectors a=⟨2,3,−2⟩ and b=⟨−3,−6,−4⟩. Select one: a. ⟨0,2,−3⟩ b.…

A: a*b = <-24,14,-3> option 'e' is correct

Q: For the given vectors u and v, find the proj,u and proj,v. 1. u = (10, 5) and v (2, 6). V =

A: Question- For the given vectors u and v, calculate projvu and scalvu. u = ⟨10, 5⟩ and v = ⟨2, 6⟩

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

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Q: Given vectors u = <-3, -7> and v = <-1, 5>, find the resultant vector  u + v.

A: The objective of this question is to find the resultant vector when two given vectors are added…

Q: Given vectors u = <-3, -7> and v = <-1, 5>, find the resultant vector  u + v.

A: The objective of this question is to find the resultant vector when two given vectors are added…

Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: 3. Given two vectors below, evaluate the magnitude and direction of R= -4A - 28 3 4 3x -2+

A: from the graph vector A = -3i - 3j vector B = -2i + 4j

Q: A wasd.schoology.cofm/COm 5. The gas tank in a car holds a total of 16 gallons of gas. The car…

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Q: 4. If the position vectors of the three points A, B and C are (2, 4, -1), (1, 2, -3) and (3, 1, 2)…

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Q: Place the vectors a, b, c, and d in order of length, from smallest to largest. Show your…

A: We have to find length of each vectors first.