a) Sketch the curve r (t) =< 2 cos t, 2 sin t, 3 > Name the curve.

Q: 8.) What is the distance between an airplane flying at 120 feet above sea level and a turtle…

A: We find the distance between an airplane flying at 120 feet above sea level and a turtle swimming at…

Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

A:

Q: A fun ride for children follows the curve with equation y= /2 sin + V2 cos 12 +2, 0sxs 24, where y…

A: We will find out the required solution.

Q: 1 cos(t) - 2 sin(t) Find the slope of the tangent line to the parametric curve at the point

A:

Q: Find T, N and B for the curve F(t) = (5 cos(4t), 5 sin(4t), 3t) at the point t = 0 Give your answers…

A: We need to find tangent, normal, binormal vectors.

Q: tangent lines?

A:

Q: Find an equation of the tangent line to the curve at each given point. x=2-3 cos 6, y = 3 + 2 sin 8…

A:

Q: Consider the parametric curve z = cos(t) sin(t) and y = sin(t) on the domain 0 < t < . Find the…

A: x=costsint ,y=sin2t

Q: Write the function in the form y = a sin b(x - c)or y = a cos b(x-c). Find the period and phase…

A: We have to solve period,phase shift and inverse trigonometric function..

Q: Find the point on the graph of y = sinh x at which the tangent line is parallel to the line through…

A: Since you have posted multiple questions, we will solve only first question for you. To get…

Q: Can the parametric curve (t, sin t) be represented as a graph y = f (x)? What about (sin t, t)?

A: Parametric curve is (t, sint) i.e x = t and y = sint

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.