2. The study of microstructure of materials is of paramount importance to explain their properties. You have been introduced to different kinds of microscopes used for the study of materials in this course. Name them. What are the typical resolution ranges offered by these micro- scopes? What do you understand by numerical aperture? Write down an expression for the same. Why is it important?

Q: Consider the following. u= (-5, -7, -1), v = (-6, 3, -3) (a) Find the projection of u onto v. (b)…

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Q: Two vectors are given by a = 2.07 + 5.0j and b = 3.0i + 9.0j. Find (a) a x b", (b) a. b", (c) (a* +…

A: Given:a = 2.0 i^ + 5.0 j^ ................eq(1)b = 3.0 i^ + 9.0 j^ ................eq(2)

Q: The resultant vector C of vectors A and B is 20 units long and forms an angle of 40o with B which is…

A: Given that The resultant vector C of vectors A and B is 20 units long and forms an angle of 400 with…

Q: 11. Find the vector product or cross product(A x B) of the given vectors: A = 50 units, 35degrees W…

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Q: Convert Unit vector from point A(4, 60°, −1) to B(2, −30°, 3) into Cartesian coordinates.

A: The given co-ordinates are cylindrical co-ordinates. This has to converted to cartesian co-ordinate…

Q: Given two vectors A = -11.3 i + 4.71 j, B = 2.38 i - 12.97 j, find the angle (in degrees) that the…

A: Solution:-

Q: Find the direction of the given vector: A = (9.95)i + (-3.77)j Measure the angle with respect to the…

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Q: Vectors A and B are given by: A = 40.62i+ 85.71j B = 81.48i + 13.19j Find the scalar product AB.

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Q: What angle OB, where 0° < OB < 360°, does B make with the +x-axis? Express your answer in degrees.

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Q: Let Vector A = Let Vector B= Find the angle between the vector, in degrees

A: Given,  Vector A = (0,2) Vector B = (5,-5) We need to calculate, Angle between both vector =?

Q: 2 • Find the angle between each of the following pairs of vectors: (a) Ả = -2.00î + 6.00ĵ and B =…

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Q: or the two vectors: (vectors)G= 2ˆi-3ˆj+1ˆk and (vector)H= 2ˆi+1ˆj-1ˆk what is (vector)G· (vector)H?…

A: Given data The vector G is given as  G→=2i^-3j^+k^. The vector H is given as  H→=2i^+j^-k^. The dot…

Q: Given the vectors A = -5i - 3j - 8k ; B = 4i - 2j + 3k ; C = 10i -12j - 8k a. Find A x B b.…

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Q: Find the Vector projection of A= and B=

A: Given, Vectors, A = 2, 1, 5, B= 5, -2, 7 The vector projection of vector A→ on vector B→ is…

Q: (e) [p, f(f)] (f) [â, Ħ] for general potential V (x)

A: [?,?(?)]?=(??(?)−?(?)?)?[p,F(x)]ψ=(pF(x)−F(x)p)ψ knowing that ?=−?ℏ∂∂?p=−iℏ∂∂x you'll get…

Q: = Given the following vectors: A 15.0 m at 40.0° counterclockwise from the +y-axis, B=20.0 m at…

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Q: The vector product of two vectors A and B is a vector and so has both a magnitude and direction: 1.…

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Q: [Q5] Given the sum and difference between two vectors, A+B= - +5y-42, A-B=32-y-2%, find the…

A: Given the vector sum A + B and the vector difference A - B, we can find the values of vector A and…

Q: In a three-dimensional space we have a vector R ( 4ai + 3af + 5ak ). Another vector S has the same Y…

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Q: Let vector a = and vector b = . The the cross product of vector a and b.

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Q: Find the vector v in the xy-plane with magnitude 5 if the angle between v and i is 150°.

A: Given data: Magnitude of the vector, v=5 Angle, θ=150°

Q: 6 units and is in the direction of +x-axis. Vector B has a magnitude 4 units and lies in the…

A: Given:- Vector B lies in x-y plane at an angle 30°with x-axis To find:-       Formula used:-

Q: Find the angle between vectors for the following. (Enter the smallest positive angle for each in…

A: (a) The angle between the two vectors can be found by taking the dot product of the two vectors and…

Q: (b) Refer Figure Q1 (b), identify the direction and plane by using Miller Indices method. (ii) 1/2…

A: (i) The length of the vector (from the initial point of the vector) on the respective axis are :…

Q: 1.43. Find the angle between each of these pairs of vectors: (a) A = -2.00î +6.00ĵ and B = 2.00 -…

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Q: Let vector a = &lt;5,2,4&gt; and vector b = &lt;-4,2,0&gt;. Find vector 2a+3b

A: The objective of the question is to find the resultant vector of 2a+3b, where a and b are given…

Q: Vectors A and B are given by: A = 89.23i + 32.22j B = 57.28i + 1.98j Find the scalar product AB.

A: Given: A=89.2i+32.22jB=57.28i+1.98j

Q: The unit vector along i+j is (a) k (b) i+j (c) (d) 블

A: Given: The vector is i^+j^. Introduction: A unit vector is that type of vector which have a…

Q: Vector A = 7.2 i + 2.6 j. Vector B = 7.5 i + 7.4 j. The magnitude of the cross product i.e. |AxB|…

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Q: Vector A = (8, 4, -5) and Vector B = (-2, 3, 0). Find the angle between these two vectors.

A: Vector A=(8, 4, -5)Vector B= (-2, 3, 0)

Q: For the vectors A = 2? •38, B= 39- 5 2, and find: %3D - (a) V = A B+C (b) V (C) V

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Q: The vector product of vectors A and B has magnitude 20.0 m² and is in the+z-direction. Vector A has…

A: The vector form of the vector A can be given as, The vector form of the product of the vectors A…

Q: = 2. At any point of the curve x Tangent vector 3 cos t, y = 3 sin (ii) Unit tangent vector

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Q: A force is specified by the vector F = [(100)i + (-110)j + (70)k] N. Calculate the angles made by F…

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Q: 1- (Exercise) Given the vectors A = Ti-2), B =i-3k, and C = 2i-2j+3k, calculate the fol- (1) lowing…

A: Given, A→=7i^-2j^B→=i^-3k^C→=2i^-2j^+3k^ d. A.→B→=A→B→cosθ…

Q: 5. Find the magnitude R of vectors A and B lying in the xy plane and given by: (show solution) A =…

A: Given:A→= 2 i^ + 2 j^B→=2 i^ - 4 j^