1) a) What is vector? b) Find the gradient of r= (x² + y² + z²)² (the magnitude of the 1/2 position vector). c) What is dot and cross product of two vectors?

Q: 8. Find the vector product of two vectors A| = 50 and B| = 20, with an angle %3D between them is…

A: Vector product is defined as- A*B = |A| |B|sin(theta) A*B = 50*20*sin(45)

Q: 5. Given two vectors: A = 51-2j+2k ft and B = -3i+2j+ 4k ft. Calculate the following: (a) the cross…

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Q: 3. Given the points M (0.1, -0.2, -0.1), N (-0.2, 0.1, 0.3), and P (0.4, 0, 0.1), find: a. the dot…

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Q: Two vectors A and B are given by à = 2î + 5ĵ + 3k and B = -4î + ĵ + 3k. a. Find the magnitude of Á.…

A: Given data:  Two vectors  A→ = 2i^ + 5j^ + 3k^B→ = -4i^ + j^ + 3k^ Required: The magnitude of vector…

Q: / The vectors A and B are given by A=-2î –3j and B = i -2j. nd 1.AxB and verify thatAxB =-BxÃ. 2.…

A: Given values:- A→=-2i^-3j^ ----(1) B→=i^-2j^ ----(2) (1) Let (R→) be the resultant value of A→×B→…

Q: 1. Calculate the dot product of vectors a and b: 30.0 B (2.40 m) y 0 A (3.60 m) 70.0⁰ 2. Sam has…

A: 1.  Dot product between two vectors is given by, A'.B' = |A| |B| cos(theta)         = 3.6 * 2.4 *…

Q: You are given the following two vectors:  a = j + 2k, b = 2i - j  1. Calculate the scalar product…

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Q: Given the following three vectors: A = -9î+7), B = -61-10) and vector C has a magnitude of, 9 and…

A: Given that, The vectors A and B are A→=-9i^+7j^B→=-6i^-10j^ the magnitude of the vector C is C→=9…

Q: When is the magnitude of the vector product of two vectors the largest? When the two vectors are…

A: Solution:-  Correct options is When  the two vector s are perpendicular

Q: The following vectors; A =, B = 1- Find the cross product 2- Find the angle between Ä and B. 3-…

A: Given,  A→= -2i^+4j^+2k^B→=-6i^+4j^-2k^1. A→×B→=-8-8i^+-12-4j^+-8+24k^=-16i^-16j^+16 k^2. Since we…

Q: 1. Three vectors are oriented as shown. If | A ⃗ | = 120 units, | B ⃗ | = 40 units and | C ⃗ | = 30…

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Q: b) Convert the vector A= - ax at P(0,2,0) to cylinderical coordinat system.

A: The cylindrical coordinate system (r,φ,z) is shown below:   The transformation between cylindrical…

Q: What is the scalar/dot product of the given 3-dimensional vectors: A = (xy)i + (2yz)j + (3xz)k and B…

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Q: . Which of the following statement(s) is/are correct?   The angle between vector A and B is 90…

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Q: Let A = î - 2ĵ and B = 2î + ĵ. Compute A.B.

A: Given data:: Two vectors A→ = i^ - 2j^B→ =2i^ + j^ Required: The dot vector of A and B vector A→.B→

Q: Find the magnitude of axb if a = 2i +j+3Å and b=3i +5j - 2k.

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Q: Two vectors in Cartesian coordinates have components A=(2,3,2) and B=(4,-1,7). What is the dot…

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Q: PartA Glven two vectors A-400+3.60 3 and B 5.80 i-2.00 nd the scalar product of the two vectors A…

A: Part AThe dot product is given by,

Q: Given two vectors Á = 4î + 3j and B = 12î – 5j a)Find the scalar product A · B. b)Find the angle…

A: (a) The scalor product of the given two vectors can be calculated as,

Q: With the given three vector A, B, C. Determine the magnitude of the dot product of vectors AxC and…

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Q: If the plane passing through the points are: A (3, -2, 1), B (-1, 0, 2), and C (4, -3, 4) a. Find…

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Q: ind the angle between the two vectors = 2î + 4ĵ – 4k andB=-2î + 2j – | (= AX³ (Remember that this is…

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Q: E. Engagement Consider the vectors given below A = Ayî + Ayĵ + A,k B = Bxî + Byj + B,k Get the dot…

A: In the given question, We have to determine the dot product of given two vectors.

Q: Calculate the scalar product of vectors A and B. Illustrate with complete and correct labels (rough…

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Q: Vectors A, B and C are defined as follows: A = 2.5i + 3.6j – 4.3k; B = 2.5i – 5.6j + 2.2k; C = 8.4i…

A: A→=2.5 i^+3.6 j^-4.3 k^ B→=2.5 i^-5.6 j^+2.2 k^ C→=8.4 i^+8.5…

Q: Which one is true for the triple product A (Bxč)

A: We know that dot product of two vectors is a scalar quantity. B→×C→ will give rise to a vector which…