1. a. How do you add two vectors a and b geometrically? Illustrate using the two diagrams. (Hint: Apply two different laws.) в b b. How do you add two vectors a and b algebraically?

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

A: We have to find which formulas involving vectors  a→,b→,c→ and vector a→ does not equal to zero…

Q: Is the following is "meaningful?" (By meaningful, I mean it could be calculated. It is "meaningful"…

A: We have given the expression (3v)×(u.b) where all bold letters are vectors, which means v,u and b…

Q: |Given the vectors a = (1,2, 3) and b = (1, –1,2), what is the dot product a - b · a? 4 5 14 (7, 1,…

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Q: If vectors A = (1,2,4) B = (3,4,1) and A+B+C = (3,2,-1) what Is C? Explain.

A: According to question,Given vectors A = (1,2,4) B = (3,4,1) and A+B+C = (3,2,-1)

Q: 1- Given the vectors A=[2, 3, -5], B=[8, -4, 3], and C=[-6, -2, 0], simplify or evaluate the…

A: We have to evaluate the following

Q: Find the best approximation to z by vectors of the form c, v, + C2 V2- 3 3 1 - 5 1 - 2 V2 = 4 - 2 3…

A: To Find the best approximation to z by vectors of the form c1v1+c2v2.

Q: A triangle in R3 has two sides represented by the vectors = (1, 3, –2) and = (2, 7, 3). Determine…

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Q: (b) Write the following vectors as linear combinations of 21, 22, and 23.

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Q: Let a and b be vectors in R3 with Ja| 3 and = 4. If the angle between a and b is |b| (2а + b) . (а —…

A: Given |a| = 3  and  |b| = 4 And the angle between a and b is pi/3

Q: 3= (5,-2) v=(-3,8) w+v If we add the two vectors, what's the correct visual representation of that…

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Q: 2 3 Given the following three vectors u = 10 v = -5| and w = 6 8. [-22]

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Q: Is the following is "meaningful?" (By meaningful, I mean it could be calculated. It is "meaningful"…

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Q: Q2: Use vector to check whether the points A (4,3,2), B (4,3,0), C (4,0,0), and D (4,0,2) are…

A:

Q: Suppose a,b and c are vectors then a.(bxc)= -(a.(cxb)) 0 صواب İhi O

A: We know that if a , b and c are vectors then

Q: If two vectors ? = 4? + 6? − 8? and ? = 6? − 8? + 4? are added together describe the characteristics…

A: If two vectors ? = 4i+ 6j- 8k and ? = 6? − 8? + 4? ar

Q: use your understanding of head to tail construction to simply the following statement down to a sum…

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Q: 39. Given a = (3, -4) and b = (1, 2). Find the vector 2 a. (3,4) a. b. 2,4) c. (6,-8) d. (5,-2)

A: From the given statement,

Q: Three vectors are given: A =il+j2+23,B= &4-§2+23, and C= -x4. Calculate: (a) A+B+C. (b) A+B-2C. (c)…

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Q: a, b, c are non-zero vectors and a is perpendicular to both b and c. If |a|= 2, \b|= 3, |c|= 4 and…

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Q: Given the vectors a = (1, 2, 3) and b = (1, –1,2), what is the dot product a · b · a? 4 14 (7,1, –…

A: a=(1,2,3)  and b=(1,-1,2)a.b.a  is dot product of three vectors

Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? EN B 3 4 nob C…

A: Given:

Q: 1 4 Let v, V1 v2 V3 - 4 V2 V3 - 5 p= - 2 and A = %3D 4 60 56 a. How many vectors are in {v,, V2,…

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Q: Find the sum of the vectors and illustrate the sum geometrically.u = (−1, 4), v = (4, −3)

A: Given Data The first vector is u= (-1, 4). The second vector is v= (4, 3).   The expression for the…

Q: Find the sum of the given vectors. a(-2,5) b (7,-2) a+b=?

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Q: Verify that the vectors a, b, and a + b satisfy the triangle inequality. Since ||a + b|| - , and…

A: Given: a= 2i+jb=i+3j

Q: 7. Sara wants to show that (a × b) × ĉ ‡ â × (6 × č). Yasmina says that it is impossible and comes…

A: This question from vector calculus.

Q: In R, you are given the vectors -10 u = 4 and v = -7 -39 If w = -9 belongs to Span(u, v), then what…

A: Consider the provided question, vectors,u=-34-4  and  v=-10-7-4and if w=-39-9z  belongs to Span…

Q: In the accompanying figure, it looks as if v1 + v2 and v1 - v2 are orthogonal. Is this mere…

A: Given figure shown below.

Q: #8

A: From the given information:u, v , w are the three vectors in R3. So let,

Q: State the condition(s) that: a) two vectors can be equal vectors. b) two vectors can be opposite…

A: To state the conditions for a given vectors.

Q: 7. Determine if following set of vectors are bases : Justify your answer. 6. 3 4

A: Given 01-2, 5-74, 635

Q: B) If u 5i-j+k, v -5j - 5k , w -i-3j+ 2k. Which vectors are perpendicular? Give reasons for your…

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Q: 7) Given the vectors å ,b and č in 3d. Identify which of the following operation is possible or not…

A: Dot Product of vectors is equal to the product of the magnitudes of the two vectors, and the cosine…

Q: 4) Add the vectors. 22.51 130.16 7.604- 69.98 13

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Q: What is the value of B for the vector [2, 4, -6]? O a) 74.5° O b) 57.7° O c) 143.3° O d) 36.7°

A: Given vector : [ 2, 4, -6 ]. Compare the vector with [ x, y, z ]. Therefore x = 2, y = 4 and z = -6.

Q: 2 3 Given the following three vectors u = 10], v = -5 and w = [-2. ..

A: Formula: Angle between the vectors u and v is given by, θ=cos-1u·vuv Given: u=2100, v=0-58 and…

Q: Express ED by combinations of the vectors a, b and C. A a D E H a. -5 b. a - 7 с. C. a + d. a + 7

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the sum of the given vectors and illustrate geometrically. 12. (1, 3, -2), (0, 0, 6)

A: Now the two given vectors be <1,3,-2> and <0,0,6> . To find the sum of the given vectors…

Q: For what values of a, b, and c are the vectors; Equal?

A: Given: 2a-ba-2b6, -22a+b-2c

Q: 7. Sara wants to show that (a × b) × c = a × b × c). Yasmina says that it is impossible and comes up…

A: Check whether the given set of vectors a→=1, 1, 0, b→=1, -1, 0 and c→=0, 0, -1 satisfy the…

Q: Illustrate with an example and a diagram why a+b=6+a¯ for all vectors a and 6

A: Vector addition

Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 3 6 1 V2 = 1 V1 = - 2 4 3 - 2…

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Q: 4 4 Let v, = - 3 V2 = 1 V3 = - 6 p = 1 and A = V1 V2 V3 4 24 44 a. How many vectors are in {v1, V2,…

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Q: Assume that the vectors a, b, c, and d are defined as follows: a = (4, 1) b = (6, 5) c = (2, -7) d =…

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Q: Let a1, a2, and b be the vectors in R? shown in the figure, and let A = [aj = b have a solution? If…

A: Given that:

Q: Below is a diagram of the dotted cube with edges of leng Suppose vectors u = (3,0, 0), v = w =…

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Q: a. Is b in {a1, a2, a3}? How many vectors are in {a¡, a2, a3}? b. Is b in W? How many vectors are in…

A: The question is related to vector spaces. The detailed explanation is given below.

Q: Prove the property if a and b are vectors and m is a real number.m(a . b) = a . (mb)

A: Let a=a1, a2, a3   and  b=b1, b2, b3. This implies that,

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.