The curves 71(t) = (- 5t, t°, 3t*) and r2(t) = (sin(5t), sin(2t), t) intersect at the origin. Find the acute angle of intersection (0) in degrees. %3D

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A: Solution :-

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A: We find the point of intersection by setting them equal

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A: Hello! Thank you for the question. We will answer the first question since the exact one wasn’t…

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Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

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A: I am attaching image so that you understand each and every step.

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A: Interval.

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A: see my solution below

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A: Consider the given point as ct=cost,sint

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A: Given,

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A: Solve the following

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A: use the arc length formula for finding length.

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A: The given curve is r and differentiate with respect to theta:

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A: The provided parametric equation of the curve is as below

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A: Then plug this in the slope of the tangent formula

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A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

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A: The arc length formula is given as

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.