a. Find the unit vector parallel to the sum of the vectors a = 12, 4, -5), D = [1, 2, 3). b. Find the arca of parallelogram with adjacent sides, a = 7i -j +k and b=2j - 3k C. Let a-; - : c-: , :) |, and C=| 2 -1 3 A = B 6 3

Q: Ans. C Dt.6. Transform to cylindrical: (a) F= 10a,-8a, + 6a, at point P(10,-8,6); (b) G = (2x…

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Q: QII Given the vectors ri 8a, + 6a, r2 a,- 9a, +a, r3 -6a,-8a,-3a, find: a) ri in cylindrical…

A: NoteAs per our company guideline we are supposed to answer onlythree subparts. So  please remaining…

Q: Given vectors A a, + 3a, and B = 5a, + 2a, 6a, determine %3D (a) A + B (b) 5A - В (c) The component…

A: Given two vector  A=ax+ 3az B= 5ax+2ay-6az |A+B|=?  5A-B ?

Q: Example (Dot product / Cross product) Given E = 3a, + 4a, and F = 4 a, 10 a, + 5a., determine (a.)…

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Q: Two points A(2,2,1) and B(3,-4,2) are given in the Cartesian system. Obtain the vectors from A to B…

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Q: Given vectors T = 2a, – 6a, + 3a, and S = a, + 2a, + a, find: (a) the scalar projec- tion of T on S,…

A: First calculate unit vector for given two vectors.  Let unit vector of T be aT and S be as. Scalar…

Q: 4.) Evaluate div D at R(1.5, 30°, 50°) of the given vector field: D = 2pz² sin°o a, – pz² sin 20 ag…

A: We need to find divergence of given signal .

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A: we will use cartesian to spherical coordinates conversion matrix to transform the vector to…

Q: If the dot product between vector A and * B equal to zero then Perpendicular Parallel * = A(1,2,3)…

A: 1. if  DOT product is zero. it means both will be perpendicular. 2.

Q: In order to illustrate these definitions and operations, consider a vector field G -D уа, - 2.5 ха,…

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Q: Given vectors A = a, + 3a, and B 5a, + 2a, - 6a,, determine (a) A + B| (b) 5A B (c) The component of…

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Q: Find a. the vector component of F = 10 a, - 6a, + 5a, that is parallel to G = 0.1 a, + 0.2a, + 0.3a,…

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Q: 1. A Cartesian vector can be thought of as representing magnitudes along the x, y and z-axes…

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Q: Paragraph Styles Q2. Distance between two points P (x=-2, y = 3, z=-1) and Q(p=4, q=-50 , z-2) 3.05…

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Q: Determine the initial point of the vector whose terminal point is (3, -2, 2) 2. Find the…

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Q: Given three points: M(-1, 2, 1), N(3, -3, 0) and P(-2, -3, -4), find the ff: a. RMN b. RMN +RMP…

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Q: Given the 3-dimensional vectors: A = (xy)i + (2yz)j +(3xz)k B = (yz)i + (2xz)j +(3xy)k Determine the…

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Q: The ff vector fields are given: A = -10ax + 20x(y-1) ay B = 2x²y ax - 4ay + zaz For the given…

A: This question belongs to basic electrical . It is about calculation of unit vector .  Have a look at…

Q: D1.6. Transform to cylindrical: (a) F = 10a, - 8a, + 6a, at point P(10,-8,6); (b) G = (2x + y)a, -…

A: Cylindrical Coordinate System : The Cartesian coordinate system makes describing the position of…

Q: The vector fields are defined as A= ap +2ag +3az, B = 0.4aap +0.4ßa -6az , both vectors are parallel…

A: Given  A and B are parallel  vector  find the alpha and beta

Q: The three vertices of a triangle arelocated at A(6, -1,2), B(-2,3, -4). and C(-3, 1, 5). Find: (a)…

A: Please find the detailed solution in below images

Q: 6. Given vectors T= 2â, – 6ây + 3â, and S = âz – 2ây +âz , find : (a) the scalar projection of T on…

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Q: Q8. The unit vector normal to the plane 2x + 3y + 6z = 7 is (2ax - 3ay +6 a,)/7 (2а, - За, -6 а, )7…

A: The unit vector normal to plane is given as:

Q: Given the vector field G y az-2 x a, + 4a, and the point Q (-2, 4, 2). Find the following: i. G at Q…

A: Given G=yax-2xay+4azQ=-2, 4, 2aN=12-ax+2ay+az

Q: 8.) Express the vector field D = (x² + y?)-(xa, + ya,) in cylindrical components and cylindrical…

A: Introduction: A cylindrical coordinate system means a 3-dimensional co-ordinate system specifying…

Q: 9. Transform vector V = a, from cartesian coordinates to spherical coordinates at point P(r = 4,0 =…

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Q: Express the vector 10 B =a, + r cos 0 a, + as in Cartesian and cylindrical coordinates. Find B(-3,…

A: Given vector is: B=10rar+rcosθaθ+aϕ=Brar+Bθaθ+Bϕaϕ The given vector is in spherical coordinates.…

Q: Finf in cylindrical components: a) a unit vector at P( ρ=5, φ=53.13, z=-2), in the direction of F=…

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Q: A. Given the vector M = -10 ax + 4ay-8az and N = 8ax +7ay-2az find: 1. unit vector in the direction…

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

Q: ransform each of the following vectors to spherical coordinates (vector) at pecified points. 4аx +…

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Q: The ff vector fields are given: A = -10ax + 20x(y-1) ay B = 2x²y ax - 4ay + zaz For the given…

A: According to guidelines we are allowed to do only first 3 subparts. Please post again for remaining

Q: Points Vector Fields D = x?yax + (y + 2)ay + xyzaz A(-2,3,5) B(4,60°, 2) C(3,45°,90°) Е 3Dpsin ф ap…

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Q: Find the divergence of vector A= 5sin? a, +ra, +÷cos²Þ a, r at (2, 0, 2.5) а. 3.5 b. 2.5 с. 4.5 d.…

A: In this question we need to find a divergence of the given vector.

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

A: If two vectors are parallel then cross product between them is zero. We will use above to find two…

Q: c. Determine the vector AB for each of the following pairs of points (a) A (3,k,2) and B (y,12,5)…

A: If any two points are given then vector between them would be the difference of two points. And in…

Q: Given the vector field in cylindrical coordinate system: A = 2psinócospa, + (rcos2o-rsin²o)a, + pcos…

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Q: D1.8. Transform the following vectors to spherical coordinates at the points given: (a) 10ax at P(x…

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Q: The component of the Vector A =a, +2a, -a̟ along the vector B=3a, +4a, is Select one: a. 3. D. 8. Ag…

A: Given tha two vectors A and B as follows

Q: Given the vector field in cylindrical coordinate system: A=2psinócospa, + (rcos²o-rsin²o)a, + pcos²…

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Q: PRACTICE EXERCISE 3.6 Determine the divergence of the following vector fields and evaluate them at…

A: We need to calculate divergence for given signal. We need to calculate divergence for all 3…

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: s) Find the unit vector directed from the origin to the point (r, y, z) = (1,1, 1)

A: Let A be the vector from origin to the given point (1,1,1). Then we can find unit vector.

Q: Q1. Transform the following vectors into spherical coordinates and then evaluate them at the…

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Q: 1. Given the vectors M = –10a, + 4a, – 8a; and N = 8a, + 7a, – 2a:, find: (a) a unit vector in the…

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Q: A method of completely specifying the direction of a vector in space relative to some reference…

A: This question belongs to electro magnetic field theory . It is based on the concept of angle…

Q: Given the vector field in cylindrical coordinate system: A = 2psinocosoa, + (rcos o-rsin o)as + pcos…

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Q: Given F = z2cos φ aρ + ρ z aφ + ρ2 sinφ az. The divergence of vector F is : (__________2 cosφ)/ρ+…

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Q: Consider the vectors A =4a,+2ka,,ta, and B = a+4a,-16a, what value of k the two vectors A and B will…

A: Need to find K value

Q: Q1) Transform the vector to cylindrical coordinate system: - K= yx'+xy + (x²//x²+y*)z° Q2) Express…

A: NOTE : Since you have posted multiple independent questions in the same request, We will solve the…

Q: Problem solving. Show your solutions and box your final answers. 1. Find the gradient of the scalar…

A: note:-As per our company guidelines we are supposed to answer only first 3 subparts . Kindly repost…

Coulomb’s Law

Coulomb's law states that the attraction or repulsion force between two charged things is proportional to the product of their charges and inversely proportional to the square of their distance. It has an effect along the line that connects the two-point charges.