Find the unit tangent vector T(t). r(t) = t'i + tj + k, P(4, 2, 8/3) T(2) = Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list. Use t for the variable of parameterization.) DETAILS LARCALC11 12.2.020. MY NOTES ASK YOUR TEACHER Find the following for the given equation. r(t) = (2 + 5t)i + (t2 - st)j (a) r'(t) = (b) r"(t) = (c) Find r'(t) - r"(t). O Type here to search 10:19 AM 8/2/2021

Q: 2.) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

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Q: Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented…

A: From x = √t we get t=x2 Then we plug it in y=t-1  So, y=x2 - 1

Q: Find the exact length of the curve described by the parametric equations. x = 1 + 6t2,    y = 5 +…

A: Find the exact length of the curve described by the parametric equations.x=1+6t2,y=5+4t3,0≤t≤3Using…

Q: Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented…

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Q: curve generated by the parametric equations. Indicate with an arrow the direction in which the curve…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: When two or more dependent variables depend upon an independent variable, then that independent…

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Q: Find parametric equations for the line segment joining the first point to the second point, where t=…

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Q: Consider the parametric equations below. x = t? - 5, y = 3 - 4t, -3 sts4 (a) Sketch the curve by…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: The given parametric equations  and .We have find the rectangular equation and sketch its graph with…

Q: Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: der the parametric equations below. x = t2 - 1, y = t + 3, -3 sts 3 (a) Sketch the curve by using…

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Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t2,    y = 3 +…

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Q: 1. Two-part question: a. Graph the parametric equation. x = −t, y = f² +1+1; only on the interval −1…

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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.