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: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin²(t)) at t = 3…

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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: Let 2ry + T sin y = 27. a) Verify that the Po(1, 7/2) is on the given curve. b) Write down equations…

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Q: Q1: for the position vector cos³ (t)i + sin³ (t)j, 0<t</2. Find the vectors T, N, B and the length…

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Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

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

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Q: The curves 71(t) = (- 5t, t°, 3t*) and r2(t) = (sin(5t), sin(2t), t) intersect at the origin. Find…

A: Answer

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin (t)) at t = 3…

A:

Q: Let a(t)-(1+t,t?,2+t?), then the equation of the tangent line at t-1 is: (2+t,-1+2t,3+2t)…

A: Here, a'(t)=(1,2t,2t)a'(1)=(1,2,2)anda(1)=(2,1,3)

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)=&lt;t+1,t,1t&gt;=&lt;x, y,…

Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…

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

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

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Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)

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.