1) Which of the following expressions represent vectors? (Zero or more options can be correct) r a) v E b) AB r d) AB" + 3jv| r e) -PQ" E ) 2u + AB 2) How many different vectors are drawn here? 3) The two vectors a dn b are perpendicular. If a has magnitude 8 and b has magnitude 3 what is |a-2b| ? 4) In which of the following cases is the length of a+b strictly smaller than the length of a-b? (zero or more options can be correct)

Q: Given the vectors r,=3i-2j, r2=i+3j, r3=3i-2j, r4=-i+2j, Indicate if these vectors are parallel,…

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Q: .If the position vectors of the points A, B, C, D are a = i+j+k, b 2i + 3j, c= 3i+ 5j - 2k, d k-j.…

A: Given:  a=i+j+k, b=2i+3j, c=3i+5j-2k, d=k-j We know that if A=x1i+x2j+x3k, B=y1i+y2j+y3k then…

Q: The parallelogram determined by vectors a and b has area 2sqrt3. If the vector c=a+b makes an angle…

A: Given information: The parallelogram determined by vectors a and b has area  23 Vector c=a+b make an…

Q: It is known that the area of the parallelogram P formed by the vectors u and V is 14 square units…

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Q: Given the cross product of 2 vectors u and v is, u × v = −3i + 2j – k, and their dot product is, u ·…

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Q: Suppose U and W are vectors in R" then ||U +W|| = ||U|| + ||W|| if the angle between U&W is equal…

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Q: For what value of m, the vector 4i + 2j – 3k and mi - j+ 3k have same magnitude? Given the points A…

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Q: The angle between two vectors a & b is 0 and the magnitude of b is half of magnitude of a . If = ā-b…

A: Given: Angle between a→ and b→ is θ……1Magnitude of b→ is half of a→……2c→   =a→-b→……3a→=a……4

Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

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Q: For the vectors v= (3,2)  and w= (-4,1) : What is the angle between v and w? Show all work.

A: According to our company's guidelines, I can only answer first question since you have asked…

Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1:4, 3:2 and 3:7…

A: If the position vectors of A and Bare a→ and b→ then the position vector of point P divid.ing AB in…

Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: Given vectors ū = [3,2, –1] and v = [-2,2,4] , calculate the following: %3D %3D a) 2ū + 30 b) ū · v…

A: Use vector properties.

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b),…

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Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: 2. In a regular hexagon ABCDEF point G is the midpoint of line segment EF, point S is the…

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Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1 : 4, 3 : 2 and 3…

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Q: What is the angle of vectors A=5m West and B=15m 60° North of West?

A: The vector A can be written as: a=-5i The vector B is 60 degree north of west that means it makes an…

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

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Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

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Q: 2. In the trapezoid ABCD point E is the point of intersection of diagonals AC and BD. If AC=14,…

A: In the given trapezoid ABCD, two diagonals AC and BD intersect each other at point E.  The diagram…

Q: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: Given that the vectors a=(6,-1,2k)  and b=(-1,k+1,4) are perpendicular, what is the value of k?

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Q: 9. The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1:4, 3:2 and 3:7…

A: Given: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1:4, 3:2 and…

Q: The angle between vectors (1,-1,–2) and (0,4, –3) is, approximately,: Select one: a. -1.41 O b. not…

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Q: The points D, E, and F divide the sides BC, CA, and AB of a triangle in the ratios 1:4, 3:2, and 3:7…

A: The points D, E, and F divide the sidesBC, CA, and AB of a triangle in the ratios 1:4, 3:2, and 3:7…

Q: Given the vectors u= 6i-2j and v=-i+9j, find 3u and u+v. Write your answers in the form ai+bj. 3u =…

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Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: Consider two vectors u, v, and is the angle between them, which of the following is false A. 00 if…

A: Given two vectors u→,v→ and θ is the angle between them

Q: Given two vectors a = (−2, 1, 3) and b = (3, −1, 2), does c = (−18, 7, 1) lie on the plane…

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Q: Suppose that u and V are vectors of lengths 2 and 3, respectively. If the angle between u and V is…

A: Dot product of two vectors u and v is given by

Q: If the volume of the parallelepiped determined by the vectors d, b, čeR' is a cubic units, which of…

A: Given, 2a→∧b→∧b→∧c→ Let, 2a→∧b→=u→ Now simplifying the given equation by apply the vector dot…

Q: For the glare Find # Ptrtmetril turoush fusses vectors Caprescatatih te pont ,4,3) 2 contahs

A: Given: Point (1,4,3)Vectors:a=3,1,-1b=0,3,5

Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

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Q: If c = 14, is the vector 2i + 5j in the span of ci – 12j and 7i - 6j? If c # 14, is the vector 2i +…

A: Answer

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b…

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Q: Given that the angle between the nonzero vectors đ = (u,,u2,u3), b = (u3.U2, -u,) is find the…

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Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

Q: 15. 16. Civen: T is the midpoina of W 1. Yes yes no Cret incuted) a. b. A DCEAPAE b. AOGA VOS b. A…

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Q: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

Q: The parallelogram determined by vectors a and b has area 2/3. If the vector c= a+bmakes an angle of…

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Q: Find the value of a so that vectors U = ai + 12j and V = 31 + 9j are perpendicular. a =

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Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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Q: 8. In triangle ABC, the point D is the midpoint of BC and E the midpoint of AC Vectors are marked as…

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Q: Given the vectors v =i+ 3j – 2k and w= 3i – 4j + k. Find the area of the parallelogram with sides…

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Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1 : 4, 3 : 2 and 3 :…

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Q: On the sides of a triangle ABC, squares ABDE, ACFG, BCJK are constructed externally to it. BF, AJ,…

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Q: (2) The two vectors u and v are shown. (o) |v= 3 45° Ju|=2 (a) Find u v (b) Find v· u (c) Is u x v…

A: To find u. v,  v. u and( u x v).

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.