Evaluate the line integral ſc F · n ds, where the vector field F(7,y) = (tan-" (y) +æ?, z*y) and C is the circle r? + y = 4. n is the outward unit normal vector to the circle.

Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: The differentiable function f(*, y, z)= 1x² +7y +3z +4xyz tangent vector v, with i = (1,2,3) e R',P…

A: We have to calculate the derivative of f

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

A:

Q: 3. Turn in: Find the equation for the tangent line to the curve defined by the vector-valued…

A: We have to find the tangent line For this we doing derivative.The procedure is given below

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.