Consider the vectors V1, V2, V3, and b. V1 4 V2 = 5, V3 6 ,b = 7

Q: Find the distance between the two vectors: u = (-5, 6, -5), v = (-3, 4, 5) Select one: O A. 2/41 O…

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Q: The dot product of vectors p = (3, -5) and q = (15,9) is A/

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Q: For the pair of vectors, find U + V, UV, and 3U - 4V. U = (-7, 0), V = (0,5) U + V = U-V= 3U - 4V =

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Q: sketch the vectors −→AB and −→P Q, and determinewhether they are equivalent  A = (5, 8), B = (1, 8),…

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Q: Find the vectors u + v, u-v, and 5u | u = i + j, v = -j – 2k %3D u + v = u - v = 5u

A: The given vectors are

Q: Find the vector PP,: 5. P, P2 12 2 4 6. 4

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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: For the pair of vectors, find U + V, U − V, and 2U − 3V U = 9, 5, V = 9, −5 U+V= U-V= 2U-3V=

A: We know that for two vectors a→=a1,a2 and b→=b1,b2, a→+b→=a1+b1,a2+b2         ⋯⋯1a→-b→=a1-b1,a2-b2…

Q: Find the requested vector in R2 where A = (-3, 6), B = (8, –6) and C = (7,4). -2AB + 7CB = help…

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Q: Find the vectors T, N, and B at the given point. r(t) = re) - (2. 20,0). (1, - 3 -1) T = N = B =

A: Here we have to find,  Unit tangent vector T→(t)=? Unit normal vector N→(t)=? Unit Binormal vector…

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Q: Find 3u, -4v, u + v, and 4u – 5v for the given vectors u and w u = i + j, v =i -j 3u = %3D -4v = u +…

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Q: write the given vector in terms of i and j. u= (-8,5).

A: It is given that, the vector u is, (–8, 5).Assume that, the symbol i represents the horizontal…

Q: Determine whether the given vectors are perpendicular. = (0, –7), 3 (8, 0) y = O Yes O No

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Q: 1. Assume the lengths of the vectors 2a – b and a + 3b , assuming a = (2,1,3) and b = (-1,2,2)

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

Q: Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ

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Q: Write w = (3, -1,1) as a sum of two vectors, one parallel to v = (2,1,2) and the other perpendicular…

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Q: Use the vectors u = (5, –3) and v = (8,2) to find the following: u+v= help (vectors) help (vectors)…

A: Answer to the question as follows:

Q: Determine whether the vectors v1=[1 2 1]^T , v2=[10 2]^T and v3=[5 6 7]^T are

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Q: sketch the vectors −→AB and −→P Q, and determinewhether they are equivalent A = (1, 4), B = (−6, 3),…

A: Given, A=(1,4), B=(-6,3) P=(1,4), Q=(6,3)     Sketch the vectors AB→ and PQ→, and determine whether…

Q: For two vectors a and b, V

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Q: Find 2u, -3v, u+v, and 3u-4v for the given vectors u and v simple

A: Given vectors are u=<3,2>and <9,1> Now, we will find the given value.…

Q: 6. Given the following vectors, Draw: a) a-b b) 2c + a c) - (c-b) a X b of

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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.

Q: 1. Assume the lengths of the vectors 2a – b anda+ 3b , assuming a = (2,1,3) and b = (-1,2,2)

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

Q: Find the length of the vector. v= (4, 3) M -| 43

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Q: Consider the vectors v, V, V3, and b. 2. 4V2 4 V1 Vg 6 ,b 7 b = | [8 9.

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Q: Find the length of the vectors (a) –2 i + 2j – 4 k: length = (b) 0.47 – 0.4 + 1.6 k: length =

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Q: 1 Let vi 6 and v3 7 V2 -1 4 3

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Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: Find the length of the vectors (a) i +3j+ k: length = (b) i — 2.6 j + 2.6 k. length = -

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Q: Find the sum of the vectors. u = (4, –1), v = (-1, -4) u + v = Illustrate the sum geometrically. y y…

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Q: 1) Check whether the vectors 효-1 33 5], -[3 10 6 T T Va = [2 7 3 2]' are line orly independent.

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Q: Find the distance between the two vectors. u= (-6, – 1), v =(1, - 6) O A. 37 О В. 37 О С. 74 O D.…

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Q: Use the vectors  u =  3, 4  , v =   −4, 1  , and w =   3, −1    to find the indicated quantity. (v…

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Q: For the pair of vectors, find U + V, U – V, and 3U – 4V. U = (3, 1), V = (-6, 2) U + V = U - v = 3U…

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Q: Find 2u, -3v, u + v, and 3u - 4v for the given vectors u and v. u- 31, v- 2i - 9j 2u - -3v - 3u - 4v…

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Q: Write w = (3, -1,1) as a sum of two vectors, one parallel to v = (2,1,2) and the other perpendicular…

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Q: The area of the parallelogram with vectors R(1,2,-1), P2(4,2,-3), P3(6,-5,2).P4(9,-5,0) is a) 998 b)…

A: Consider the given vectors P11,2,-1,P24,2,-3,P36,-5,2, and P49,-5,0. Use the given vectors and draw…

Q: Perform the following operations on the vectors ū = (5, –2, 1), v = (-1, –2,0), and (3, 3, –4). w =…

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Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

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Q: Perform the following operations on the vectors (3, 2, −4), v = (-1, 5, −2), and = (0, 4, 2). ū = ū.…

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Q: Find a unit vector ū that has the same direction as the vector i = (-3, 3, - 3 -3 2 А. 22 22 22 3 B.…

A: find the magnitude for finding the unit vector.

Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: Find the distance between the two vectors. u = (4, – 8), v = (- 8,8) O A. 100 О В. 4 Ос. 20 O D. 400

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Q: b Write the vector b in terms of the other vectors. C.

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Q: Find the vectors T, N, and B at the given point. r(t) ) =(2², ²32²³, t), (4,- 15, -2) N = B =

A: This question can be solved by applying the formula of T,N,B

Q: o -3 - 5 ↓ 2 buy on IN A 65 US

A: We have to find out the components of the addition of the two vectors, that is, w→+v→.

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.