Q1:- Find T(t) and N(t) for the curve helix x = a cos t, y = a sint and z = ct, and then find B(t), at and an.

Q: b. A curve is given by the equations, where t is a parameter: x = 3t2 + 4t y = sin2t i. Find in…

A: A curve is given by the equations                                    x=3t2+4t…

Q: Q4] (15Marks) Sketch the curve r cose. %3D

A:

Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

Q: Find the intrinsic equations of the curve x = (alcos (je, + a(sin fje,+ bes). aff Ans. 4120² +65ji/2…

A: Introduction: Intrinsic equations refer to a method of representing a curve or surface in terms of…

Q: 3t? Find the length of the curve x = t, y 2 osts 13. 3 =

A:

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

A:

Q: 21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the…

A:

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: For the curve a = 4+ 2t², y = t³ + 3t² – 3t choose two statements that are correct. The curve is…

A:

Q: Q4: Find the angle between the tangents to the curve R(t) = t²i+ 2tj – t³k at the points t = F1

A:

Q: 4x2-4xy+y2-6x+8y+13=0 find this curve's  central  coordinates

A: Given,    4x2-4xy+y2-6x+8y+13=0   It is a equation of parabola.

Q: Find the length of the curve. r(t) = (7t, 3 cos t, 3 sin t), -2 ≤ t ≤ 2

A:

Q: Given the parametric curve r (t)=⟨sin(πt),t⟩ where −1≤t≤1, find r ′ (t) and sketch the curve,…

A: The given curve is, rt=sinπt,t where -1≤t≤1. A tangent vector shows the direction of the motion. The…

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.