Find a method that uses the Dot-Product to decide for three randomly chosen points P, Q, and R in 2-space, if they all lie on a straight line, or not. Describe how you'd do it, and explain why it works. Hint: Use the vectors PQ and QR. Picture!!! What adjustments need to be made if you are in 3-space, or in higher dimensions?

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: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Find eguation of a Plane that an contains the vector: and and Z=3E

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Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find the area of the parallelogram determined by the vectors u and v.

A: Given any non-zero vectors.

Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: Use paper and pencil to identify the redundant vectors. 4 3. 0. 0.

A: Definition : Redundant vector in a set is a vector which can be written as linear combination of…

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

A:

Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non-orthogonal because the dot…

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Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: Find the area of the parallelogram that has the vectors as adjacent sides. u- (3, -5, 3) v = (2, 0,…

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Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: a) Given: v1=<-3,6>,…

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: The area of a parallelopiped that is formed by two vectors A and B can be obtained mathematically…

A: It's area of parallelopiped is given by A×B.

Q: Find the dot product of vectors and .

A:

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: (a) the dot product of the two vectors a(-2,5) and b(3,6) a · b = ax · bx + ay · by = -2 · 3 + 5 ·…

Q: can you add 3 vectors using the parallelogram method? support you answer

A: Parallelogram law : if two vector quantity are represented by the two adjacent side of a…

Q: Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B × A).C,…

A: Cross product of the vectors

Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: Find the acute angle formed by two diagonals of a cube. (vectors) show complete solution.

A: It has been assumed that the length of each side of the cube is a unit.

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (– 6, – 1, 3), Q = (- 1,…

A: The corresponding position vectors with respect to origin are,…

Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

A:

Q: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…

Q: Find the area of the parallelogram that has the vectors u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

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Q: Find the measures of the angles of the triangle whose vertices are A = * .(-1, 0), B = (2, 1), and C…

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: 1. What is the appropriate dot product technique for both Cartesian and Geometric vectors?

A: Given

Q: Find volume of the parallelepiped determined by the vectors a = (8, 1,0), E b = : (1,4, 1), and c =…

A: The given vectors are a=8,1,0, b=1,4,1 and c=1,1,10

Q: Find the dot product of the vectors v = 5i - 3j and w = 2i - j.

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Q: b. Please provide a well explained answer for the follwoing. And explain how to add/subtract…

A: We have to write definition and some basic properties of vectors.

Q: Find the area of the parallelogram that has the vectors u (2,-1, 3) and v (4, -5, 1) as adjacent…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

A:

Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.