Find r'(t), r(t), and r'(t,) for the given value of to: Then sketch the space curve represented by the vector-valued function, and sketch the vectors r(t,) and r'(t,). r(t) = ti + tj + k, to = 2 r'(t) = r(t,) = r'(t,) = -2 2- y -2. -4, -6, 4 -8 -8 r" C y 4. -4 r -2 -2

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

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Q: Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x,…

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Q: If/Given that → F(t)=(5t+3,3t²,8-4t³), Find: - a) The first derivative: b) The first derivative: c)…

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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: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

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Q: the position vector r describes the path of  an object moving in space. (a) Find the velocity…

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Q: Let f(x, y, 2) = cos(ryz) Find the directional derivative of f at the point (,, 7) in the (a)…

A: We have to find Directional Derivative and Largest possible value.

Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: Find r'(t), r(t,), and r'(to) for the given value of to. r(t) = (1 + t)i + t°j, to = 1 r'(t) = r(t,)…

A: Here is the solution of the given problem. Space Curve:

Q: consider the vector-valued function r(t) = a) State the domain of r(t) b) Identify where r(t) is…

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