Show that the following vectors are orthogonal: Ā= 4a, + 6ã, – 2ã, and B= -2ä,+ 4ã, + 8ã:

Q: Given the two vectors M= 5a, – 2a, + 4a, and N=- Sa, –7a,+2a,. The unit vector in the direction of…

A: Given Data: M = 5ax -2ay +4az N= -8ax-7ay+2az

Q: If A = ax + 3az and B = 5ax +2ay - 6az. Find the Dot product of vector A and B

A: This question belongs to basic electrical . It is based on the concept of basic laws of vector…

Q: [Q1]Find the type (source, sink or parallel) of the following vector fields 1- F=yzax – 2yay +xyaz…

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Q: Add and subtract the following vectors given in rectangular forms and illustrate the graphically. A…

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Q: If A = 3a, + 2a, - 6a, and B = 4a, + 3a, determine %3D (a) A B (b) A X BỊ (c) The vector component…

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Q: Q1: Three vectors extending from the origin are given as ri = 7ax + 3ay –- 2az r2 =-2ax + 7ay – 3az…

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Q: 14. If the angle between the vectors A = xâ +â andB = V3â +â is 60°, find X,

A: We need to find out value of unknown for given angle

Q: The following vectors are given: M=-10ax+4ay-8az and N=8ax+7ay-2az. Find the unit vector in the…

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Q: For any vectors u and v in V3, [u v = |u ||v|. %3D

A: Here vecctor are given need to prove

Q: 3\ Find A that makes the two vectors : u = 2i + 3j – 4k ü= 3i - Aj +3k orthogonal ?

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Q: نقطتان )2( The angular separation between the vectors A = 2 ax + 3ay + 8az and B = 4ax – 3ay %3D +…

A: " Since, you have asked multiple questions, we can solve only one question at a time. Kindly, repost…

Q: Consider the vectors A 4ax+2kay+az and B = ax+4ay-4a, what value of k the two vectors A and B will…

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Q: Two vectors "A" and "B" are in x-y plane and the angle from the vector B to A is 30°, measured…

A: We need to select correct option.

Q: A Moving to another question will save this response. estion 19 The vector fields are defined as A=…

A: Given  Two vectors are parallel find alpha and beta value

Q: 2. If A = ax + 3az and B = 5ax +2ay - 6az. Find the Dot product of vector A and B O 120.6 degrees O…

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Q: What is the resultant of vector A=2i +2j, and vector B= -2i+lj Select one: a. 3.5 b. 3 C. 5√2 d. √26…

A: Given data, A=2i+2jB=-2i+1j

Q: Given these two vectors A = -10 ax + 4ay – 8az and B = 8 ax + 7ay – 2az, find: a.) Unit vector from…

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Q: ri = 2a, + 4ay 5az r2 = ax + 2ay + 3a, Find the unit vector parallel to the resultant of vectors and…

A: We need to find out unit vector of resultant vector .

Q: Given the vectors below, find A • B A = 15a, + 12a, - 5az B = 10a, - 8a, %3D Select the correct…

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Q: Question 17 The vector fields are defined as A= ap +2ao +3az, B = 0.1aap +0.1Bao -6az , both vectors…

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Q: (a). F = y³ ax + xyay - zaz (b). F = x² ax + 2zay - yaz

A: Curl of two vector field is calculated by taking the cross products of the two vectors , curl is…

Q: 5. determine if the two vectors are parallel, orthogonal or neither a) q = (4,-2,7), p = -3i +j+ 2k…

A: a) Given  Two vectors  q=4i-2i+7p=-3i+j+2k

Q: Represent the following quantities by vectors: 5 sin (2nft-1); 3 cos (2nft+1); 2 sin (2nft+2.5) and…

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Q: Check whether the two following vectors are parallel or not: A=(-2,1,-1) B=(0,3,1)

A: The given vectors can be written as

Q: 2. Explain if these vectors A = 4i - 2j + 4k and B = 4i + 3j are parallel perpendicular or not?

A: It is given that: A=4i-2j+4kB=4i+5j

Q: The vector fields are defined as A= ap +2ao +3az, B= 0.25aap +0.25ßam -6az , both vectors are…

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Q: 2. Convert the vector A RAR+0 Ao + A into Cartesian coordinates.

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Q: Q1 Given A= 3i-7j+5k, B = -i+7j-k, C= 4i-j+k. Find the unit vector of: (a) А-В+С (b) АхСxВ

A: According to the question we have to calculate the value of given vector calculations.

Q: The vector fields are defined as A= ap +2ao +3az , B = 0.25aap +0.25ßag -6az , both vectors are…

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Q: The vector fields are defined as A= ao +2ao +3az, B= 0.1aap +0.1Bao -6az, both vectors are parallel…

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Q: If only the cross product of two non-zero vectors is zero, then these vectors are prove that it is.

A: If only the cross product of two non-zero vectors is zeto then these vector are parallel to each…

Q: QI: Find all unit vectors parallel to JZ plane and perpendicular to the vector ū = 5i -j + 2k %3D

A: Vector which is parallel to YZ plane is, This vector is perpendicular to Therefore, dot product of…

Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: * i-10j+6k

A: From the question  Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3   Let n1 and n2 are two normal of plane 1 and…

Q: ctor A-2ax+ay+2az and vector B=2ax+ay+2az, the cross product of A and B is

A: Here the ans is option d.

Q: Give a reason why the dot product of two vectors is known as the scalar product

A: Suppose there are two vector that is A and B, A→=Axi^+Ayj^+Azk^B→=Bxi^+Byj^+BZk^ Now, multiplying…

Q: Q4. Which one of the following vector function has divergence and curl both zero A 2xza, – yzay 2 az…

A: vector field F=⟨f,g,h⟩ Divergence of a vector function F is: The Curl of a vector function F is:…

Q: The vector fields are defined as A= ap +2ao +3az, B = 0.1aap +0.1Bao -6az , both vectors are…

A: Given  Find the value of alpha and beta

Q: The vector fields are defined as A= ap +2ao +3az, B = 0.5aap +0.5ßam -6az , both vectors are…

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Q: 2. IHA - 24, + 6a, – 3a, and B = – 3a, - 4a, - Sa,, find: (a) a unit vector in the direction of A -…

A: According to question: The given question is

Q: When two vectors are perpendicular

A: Here the ans is a.

Q: c). Show that the vectors A and B are parallel A = 2i +4j + k ; B = 4i + 8j + 2k d). Prove that curl…

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Q: The vector field pattern of A = 3yax is Y4 YA

A: Given data:

Q: 277 Give A= -i+3sin-j-2 cos k, B=-3i-5ln2 j- 4 k, C= 4 3 Find the unit vector of the following: (a)…

A: GivenA=-i+3sinπ3j-2cos2π3kB=-3i-5ln2 j-4kC=4i-5j+5k

Q: the constant 'c' such that the vector : = (x + 5y) âx + (y − 3x) ây + (x+cz) â will be solenoidal.

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Q: 4. determine the angle between the two vectors v= (1,2,3,4), w = (0,-1,4,-2)

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Q: Question 8 Consider the vectors A =4ax+2kay+az and B = ax+4ay-32az what value of k the two vectors A…

A: To find the value of k if A and B are orthogonal vectors

Q: The vector projection of the vector A =ax -2ay + az on the vector B = 4ax - 4ay + 7az is *

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Q: Question 18 Consider the vectors A =4ax+2kay+az and B= ax+4ay-8az what value of k the two vectors A…

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Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that r1+r2+r3 is equally…

A: It is given that: r1,r2 and r3 are three parallel vectors of same magnitude. i.e., r1→=r2→=r3→=r

Q: B/ Write a matlab code to find sum all elements of a vector, if the vector is the following: M=[5,…

A: Given,  Vector M = [5, 7, 15, 0, 55, 100, 11, 23] To find sum of all elements of vector.

Solenoidal Vector Field

In Physics and Mathematics vector calculus attached to each point in a subset of space, there is an assignment of a vector in a field called a vector field.