Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a sin t)i + (a cos t)j + (bt)k , at t = 2n. Where a, b>0

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

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Q: Consider the curve x = et-5 cos t, y = et-5 sin t, 0 <t < 2n. a) Find the values of t where the line…

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Q: x=sec(t) y=tan(t) t E[0,pi] a) Identitfy the (x,y) coordinates of the point corresponding to the…

A: To determine the coordinates of the point.

Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: The curves 71(t) = (- 5t, t°, 3t*) and r2(t) = (sin(5t), sin(2t), t) intersect at the origin. Find…

A: Answer

Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

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Q: Find the parametric equation for the line tangent to the r(t)=sinti+(t2-cost)j+etk curve t=0 at the…

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Q: Without using a graphing utility, show that the parametric curve r(t) = (3t cos(3t), 3t sin(3t), 3t)…

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Q: What is the slope at t = −2 ?

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Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t. Construct a table with…

A: Given problem:- Sketch the curve given by the parametric equations x= t3 - 1 and y= t2 + t.…

Q: . Consider the parametric curve defined for all real t by x = t³ + 1 and y = 2t + t. Find the…

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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.