16. Given the vectors u = (1,2) and v=(4,-2) in R2 find the following (Show your work): a. ||u|| b. ||v|| c. u.v I d. d(u, v) e. Angle between u and v. Recall the formula: cos(0) = UV |lu||||v||

Q: Find the two values of t that would make the angle between vectors ⟨1, −2, 0⟩ and ⟨0, −1, t⟩ equal…

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Q: (11) Three vectors given: a = (1) a+b+c, (2) a.b m 21-3k, b=4i, č-5k (3) the angle between a and…

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Q: 10. Given points. P(2,5,-1). Q(-1,-4,1), and 7(5,0,2), find: (a) the vector Reg: (b) a unit vector…

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Q: When the angle between vectors u and v is between 0° and 90°: || You can't tell O t • 0

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Q: Q1:The following vectors; Ā =, B =< 2,-4,6

A: To find the cross product of the vectors  A⇀×B⇀=ijk14-12-46 simplify…

Q: Which of the following expressions is equivalent to 2i? Select all that apply. a (2i) (2)

A: Given: x23 Now check:   a)  x32=x132=x13×2=x23 b) x3=x123=x12×3=x32 c) x2x3=x2-3=x-1 d)…

Q: 2. Find the exact angle between vectors a = 3 î - j - 2k – 18 10 b = v – w, wherev = 2î + ĵ + 4kandŵ…

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Q: 8. Determine the angle between the two vectors. a) Ã = and B = b) Ả = -2î + 3 + 5k and B = î + 2j…

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Q: Find u · v, where 0 is the angle between u and v. ||u|| = 100, ||v|| = 230, 0 6

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Q: Q9: Showthat triangle ABC is right at A where A(1,0,1), B(2,1,0), c (1, 2, 3).

A: Question No. (9):To show that triangle ABC is right at A where . Note: Since the student has posted…

Q: Determine the dot product uv, if |||| = 9 and |||| = the angle between the two ㅠ vectors is = 3…

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Q: Find u · v, where 0 is the angle between u and v. ||u|| = 4, ||v || = 64, 0 4

A: Directly use the formula for dot product of two vector and simplify the result.

Q: 4. Which vector(s) below is perpendicular to ū = 2i– 3j? A. V = 27+ 25 B. W = 31+ 25 C. Ã = 5ï – 75…

A: Given: The vector U→=2i→-3j→, To determine: Which of the following vectors are parallel to the given…

Q: Consider vectors u = (4, 1) and V = (-1, 3). a. Find the linear combination W = 2u - 3v. b. Find the…

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Q: The vector v is 10 units long and makes an angle of 30° with the positive x-axis. What is the…

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Q: of c. Calculate the angle made with the positive direction x-axis by the vector (a) v= 3₁ + 4j (b)…

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Q: 4.18. Given vectors u = 3j – - 6k and v = 6i – 4j – 2k, find the dot product of u and v.

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Q: The set { (1, -1, 1), (2, 0, 1), (1, 0, 0) } in R is a span ? Select one: O True O False Let u= and…

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Q: 4. [6.1] If vector b is shown below, sketch a vector. a) Equal to b b) Opposite to b c) With the…

A: Solution of given question is written in below steps.

Q: Find x so that the vectors u and v below are perpendicular. X u= 6 [-9 x=0 4 v=6 [-1]

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Q: 2. If is the angle between two non zero vectors u and v, where 0° s 0 s 180° then: cos 0 = U.V…

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Q: Let u =⟨2,2,1⟩which makes an angle of 30∘ with v. If the dot product of vector u and v is 6. What is…

A: Given:   To determine: The magnitude of vector v

Q: find the compoment form of vector v given ||v|| = 13 and the angle with positive axis is theta=300…

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Q: 2.) Find the angle, 0, between the vectors v = (5, 3) and u = (4,-7) by using the dot product. Round…

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Q: Ifv+w= and v = [1]. C W= , compute and draw the vectors v and w.

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Q: For the vectors ū 8 find the following: %3D a. ||u|| b. A unit vector in the direction of u.

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Q: 7.(a) A and Care the points (1,3, –2) and (4,–4,4) respectively. Point B divides AC in the ratio…

A: We find a coordinate in given ratio.