Let u = (– 3, 5, 3), v = (4, –- 5, – 2), and w = (0, 5, – 3). Assume · always refers to the dot product. If possible, find the following. If not possible, type DNE. Use < and > to enclose vectors: for example, < x, y, z > u· v = (3u) · (4v) = (v. w w) u. (3v + 4w)

Q: Determine the dot products of the following pairs of vectors. (a) (3, 5), (3, -4) (b) (2, -5, 3),…

A: Solution :-

Q: Find the vector z, given that u = (3, -2, 5), v = (0, 2, 1), and w = Z= z = −u + 4v + 1 _W 2 (-6,…

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Q: 63dx Use the trapezoidal rule with n = 20 trapezoids to evaluate I Also, 1+2x find the accurate area…

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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: Order the following vectors by increasing magnitude. (3,4) (0,-6) (-2,4)

A: Given vector is (3,4) , (0,-6) and (-2, 4). We have to order the vectors by increasing the…

Q: 9. If = 1, 4, 5) and W = (2, -3, 1 V ( − w a) 3-2W b) |v|

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Q: If A is (3,5,0), B is (-1,-2,7), and C(6,1,3) forms a triangle. Find the vector component of CB…

A: let a,b,c are position vector of point A,B,C respectively. Therefore a=3i+5j, b=-i-2j+7k c=6i+j+3k…

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: Let a = (5, 4) and b = (5, – 8). Compute the dot product. a b

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Q: If vector a= and vector b=, fınd a x b (the cross product of vector a and vector b). Enter the…

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Q: Let A = space of A. Oh=2 Oh=-2 Oh-2 1 3 0 2 -1 Oh 2 2 2-2 Oh can be any real number. . Determine the…

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Q: Among the following vector pairs shown below choose an orthogonal pair. u = (1, -1, -1) and 7 = (2,…

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

Q: Let ā = (1, – 5, 2) and b = ( – 1, 5, 3). %3D Find the angle between the vectors (in degrees).

A: We know that for two vectors a→ and b→,   cos(θ)=a⇀.b⇀|a||b|⇀⇀ where θ is the angle between vectors.…

Q: u = (7,2,-5) and v = (9,-1,-6).

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Q: Given vector u = (-3,2) and v = (-3, –1) , determine the value of v – 2u ir component form.

A: We can determine the component form as below.

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.

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 5v

A: Given that u=-3, 4  and  v=2, -5. This implies that, 5v=5·2, -5=5·2, 5·-5=10, -25 Thus, the…

Q: TRUE or FALSE: Vectors u = (-4, 1, -2) and = 1 7 1 1

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Q: Find the unit vector in the direction of the given vector. Write your answer in (a) component form…

A: According to our guidelines we can answer only 3 subparts or first questions. Kindly repost the…

Q: Find the unit vector with the opposite direction of a⃗=(8,−10,3,−1,9,3)

A: We have to find the unit vector with the opposite direction of a→=8,-10,3,-1,9,3.

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.