ind the curve's unit tangent vector. Also, find the length -(t) = (5cos t)i + (5sin t)j + (V7 t)k, 0stsa Find the curve's unit tangent vector.

Q: (a) Find an equation of the tangent(s) to the curve at the given point. x = t³-t, y = e²t + 3t+2;…

A: We will find the required.

Q: Find the tangent plane to the equation z = 2y cos(5z – 4y) at the point (4,5, 10) z = 2y- 2= 0 X…

A:

Q: (i) Determine the required initial angle of inclination (in degrees) of the projectile (ignore air…

A:

Q: Find the tangent line of the curve (- 31,1-2)at the point (2,14)and estimate y0 so that (2.1,y0)is…

A: given curve is                                                                     x=t3-3ty=t4-2…

Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

A:

Q: Locate the center of the curve r = 4(sinθ + cosθ)

A: NOTE: Refresh your page if you can't see any equations. . the given curve is ...............(1)

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=<t+1,t,1t>=<x, y,…

Q: A mouse Q runs along the positive y-axis at the constant speed v at the origin. A cat P chases the…

A: It is given that∙Mouse Q runs along y-axis with a constant velocity v1∙Cat P runs along curve C with…

Q: Determine the equation of the line tangent to y = x + tan x at the point (T, T).

A:

Q: Use the formula for the slope of the tangent line to find dy for the curve c(t) = (t−¹ – 8t, 7t³) at…

A: Explaination of answer is as follows

Q: Sketch the curve f(x, y) = c, together with Vf and the tangent line at the given point. Then write…

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.