2. Show that √²(¹) = 0 provided the distance r from a point P(x, y, z) to the origin is not equal to zero, i.e., r = √√x² + y² + z².

Q: Convert the point (r, 0, z) = (1, π, - 1) to Cartesian coordinates. Give answers either as…

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Q: 1. Show that vectors a= (4.0,-1), b =(1,3,4), and c =(-5,-3,-3) form the sides of a triangle. Is…

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Q: 4. If f is a scalar field and F, G are vector fields, prove that: V. (F x G) = G (V × F) – F (V x G)

A: f is a scalar field and F, G are vector fields

Q: 5. Evaluate the integral by making the given substitution. (Use C for the constant of integration)…

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Q: The vector product of vectors A → and B → has magnitude 12.0 m2m2 and is in the +z+-direction.…

A: The problem involves the vector product (also known as the cross product) of two vectors A and B.…

Q: A circular area S is concentric with the origin, has radius a, and lies in the yz-plane. Calculate…

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Q: 1. Review of Vectors: Right figure shows A and B. Let A+ B = C a. Determine the x and y components…

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Q: Prove that (+)* a+ib = a-ib c-id' where a, b, c, d are nonzero real numbers.

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Q: Give the rectangular coordinates of the point C (ρ = 4.4, φ = −115◦, z = 2). 2. Give the cylindrical…

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Q: Cartesian to Spherical Given a point P = (-2,6, 3) and a vector A = ya, + (x + 2)a, are in Cartesian…

A: Given: A point P=(x,y,z)=(-2,6,3) A vector A⇀=yax^+(x+z)ay^ Calculation: (a) In spherical polar…

Q: That is the angle between two vectors A and B if | A × B |= A·B?

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Q: Q2- If a = 2 i-j+ 2 k and b = 4 i- 3 k, find the magnitudes of a and b and the angle between them.

A: Given : a = 2i-j+2k b = 4i-3k

Q: Two points in the xy plane have Cartesian coordinates (6.00, -4.00) m and (-7.00, 7.00) m. (a)…

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Q: 8. A jetliner can travel 1700 mi from Fargo, ND, to Phoenix, AZ, in 4 hr with a tailwind; but it…

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Q: 47. Write as a single integral in the form f(x) dx: f(x) dx + f(x) dx f(x) dx

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Q: 19. In an orthorhombic cell, the primitive vectors are 1.27Å, 2.14Å and 1.51A. Deduce the intercepts…

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Q: Given the points A(2, -1, -3) and B(1, 3, 4), specify the vector at point A that extends to point B…

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Q: Your character starts at position po. Each frame, it moves along the normalized vector at constant…

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Q: Four vectors:  a´ = [1 2 3], b´ = [1 0 -1], c´ = [1 2 3 4], d´ = [2 1]. Compute each of the…

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Q: For any three vectors, prove that A • (B × C ) = (Ā × B) · T. Also calculate Ā • (Bx C ) for the…

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Q: Given two vectors: M = -3i + 6j – 5k and N= -2i + 3j + k The magnitude of 2N - Mis A 7.07 B 39.2 C…

A: Given: M→=-3i^+6j^-5k^N→=-2i^+3j^+k^

Q: a) what is the length of the unknown side, b) the tangent of θ, and c) the sine of φ?

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Q: Q1) Given points A(p= 5, 6 = 70°, z -3) and B(p 2, 6 =-30°, z = 1), find: (a) a unit vector in…

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Q: in plane polar 3. The point (1,1) in rectangular coordinates is equivalent to coordinates.…

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Q: Let /be the line through the point with coordinates (0,1,0) in the direction of the vector 1 0 their…

A: Given, l be the line through the point with coordinates (0,1,0) in the direction of the vector…

Q: Question ( Which of the following is a unit vector parallel to the vector? Select one: O None of…

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Q: 2. Find the scalar products ( · B) and vector products (A x B) of the following: a) A =i+2j + k and…

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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: Two points in the xy plane have Cartesian coordinates (1.50, -3.50) m and (-6.50, 6.50) m. (a)…

A: a) distance between the points AB=(−6.50−1.50)2+(6.50+3.50)2  m=12.806m b) Now we need to determine…

Q: Express the unit vector a, in spherical components at the point: (a) r = 2, 0 = 1 rad, p = 0.8 rad;…

A: The unit vector ax in spherical components is given by Where Because