Find the point on the curver(t) = (5 sin t)i + (5 cos t)j + 12t kat a distance 26p units along the curve from the point (0, 5, 0) inthe direction of increasing arc length.

Q: Find the arc length of the curve ä = Length = 7y³/²2 from y = 0 to y = 10.

A:

Q: Find the arc length of the graph of y = ln(sin x) from x = π /4 to x = π/2.

A: The formula to find arc length of a curve f(x) from x=a to x=b is, L=∫ab1+f'(x)2dx.

Q: Find the arc length of the curve y = 3e² + 12 e from a = 0 to x = 4. =

A:

Q: what is the arc lenght of  the curve y=ln(sinx) between th points x=pi/3 x = 2pi/3 ?

A:

Q: x = 2 sin-1 1, y = In (1 – r²) (0<1s!)

A:

Q: Find the arc length of the curve r 2sin () from 0 0 to 0 = 7.

A: To find the arclength of the polar curve.

Q: Find the arc length of the curve y =(2²-8 In(z)) from z = 2 to z = 5. Length = 0

A: From  to

Q: Find the arc length of the curve x = (10 – 2y)³/² ,-3 < x<

A:

Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1].

A: Solution:   Given that,      y3+y=x2+6x,  interval -5, -1         Then, differentiating with…

Q: Find the arc length of r(t) = 3 cos ti + 3 sin tj + 5t^(7/2) k

A: The given vector is r→t=3 cost i^+3 sint j^+5t72 k^....(1) To find: the arc length of the vector.

Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

A:

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.