True or False and explain 1- For any two non parallel and non orthogonal vectors a and b with angle θ  between them, it holds that  cosθ(a.b) = sinθ(axb).   2- If r(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩, then the ∫r(t)dt is equal to ⟨−2sin(2t),−cos(3t),tlnt−t⟩+C, where C is a vector constant of integration.

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A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

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Q: Consider the following vector equation. r(t) = (3t - 4, t2² + 2) (a) Find r'(t). r'(t) =

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Q: Find the vectors T and N and the binormal vector B = T x N, for the vector-valued function r(t) at…

A: Given, the vector-valued function  to find:  the vectors  and  and the binomial vector  at .

Q: YouTrylt 1 Find the derivative of the vector function. r(t) =(t sint, t, 1 cos(2t ) C.

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

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Q: Find the angle 0 between the vectors. (f. 9) = L R f(x) = 3x³, g(x) = 4x4, %3D f(x)g(x) dx radians

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Q: Find the value of x so that the vector i+2j+xk   makes and angle  pi/4  of  with the positive…

A: i+2j+xkTo Find: Value of x so that the vector makes an angle of π4 with the positive z axis.

Q: For any two nonparallel and non orthogonal vectors a and b with angle between them, it holds that…

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Q: e vector equation ū=

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Q: at Q6:- If w = xi + yj + zk nonzero vector. Then show that cos a + cos? B + cos? y = 1, where a, B…

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Q: I need help with this problem and an explanation for the solution described below. (Calculus 3:…

A: Step 1:

Q: ²=2+3+ k, v = -2i+ 3k. Find: (a) u v= (c) u x v= CONC (b) v. u= (d) 7 x = (e) Angle between 7 and 7…

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Q: 2) Let two vector functions be defined by r₁(t) = (2t, t², t²) r₂(t) = (sint, sin(3t),5t) a. Find…

A: a. Consider the given vector functions, r1(t)=2t,t2,t4r2(t)=sint,sin3t,5t if two vector function…

Q: Given ri = 3i - ej +In2 k, r2 = 5i + 7 e'j - 4 k and r3= 7i-7j+ k. Find the unit vector of (a)…

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Q: Find T(t) ,N(t),B(t), and K(t) for the vector position r(t) = (e2t cos t) i + (e2t sin t)j + 2k when…

A: Given rt=e2tcosti+e2tsintj+2k

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A: Use the formula of directional derivative.

Q: The vector F = -ar + 2a expressed in RCS and in terms of is O None of the choices O - = (−cos0sind…

A: We can solve this using spherical co-ordinate matrix

Q: For ff:R⟶R, with f(x)=3x+4f. Which of the following functions g(x) guarantee that (f∘g)(x)=x? Group…

A: Please check step 2 for the solution.

Q: Show that fi(r) = rª and f2(r) = r² +1 are orthogonal on the interval [–1, 1).

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Q: Given the vector function 7(t) = (t, sin (t) – t cos (t), cos (t) +t sin (t)) Calculate B (34)

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