Use the inner product < f, g >= = f(x)g(x)da in the vector space Cº[0, 1] to find < ƒ,g >, ||f||, |19||, and the angle Of between f(x) and g(x) for f(x) = -5x² - 6 and g(x) = −9x + 5. (f,g) = ||f|| = ||g|| 0fg radians.

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

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Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: (c) If f is a C² scalar function, then V × (Vƒ) = 0. True False (d) The lines 1₁ (t) = (1 − t, 1+ t,…

A: (C) If c is scalar function Means      curl(grad ƒ)  is = 0   Therefore correct ans is  True

Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

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Q: Consider the following function and point F f(x, y) = /E (a) Find the unit vectors in the direction…

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Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at…

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