Question

A particle moves along x=3cost,y=3sint,z=4t, find the magnitude vector.

Answer 1

Answer:

5) It is a problem that needs to be dealt

Answer 2

Therefore Magnitude vector of the particle moving along x=3cost,y=3sint,z=4t is given by  $(\frac{{\vec T}}{{\left| {\vec T} \right|}} = \frac{1}{5}\left( { - 3\sin t\hat i + 3\cos t\hat j + 4\;\hat k} \right)\)$

Given:

x=3cost,y=3sint,z=4t

To Find:

The magnitude vector

Solution:

We can simply solve this numerical problem by using the following process.

Given that:

x=3cost,y=3sint,z=4t

⇒ Equation of the curve $\(\vec r = x\hat i + y\hat j + z\hat k = 3\;cost\;\hat i + 3\sin t\hat j + 4t\;\hat k\)$

⇒ Required Vector $\vec T = \frac{{d\vec r}}{{dt}} = \left( { - 3\sin t} \right)\hat i + \left( {3\cos t} \right)\hat j + 4\;\hat k\)$

⇒ Magnitude of the Vector, $\left| {\vec T} \right| = \left| {\frac{{d\vec r}}{{dt}}} \right| = \sqrt {{{\left( { - 3\sin t} \right)}^2} + {{\left( {3\cos t} \right)}^2} + {{\left( 4 \right)}^2}} = \sqrt {{3^2} + {4^2}} = 5\)$

Magnitude vector:

⇒ $(\frac{{\vec T}}{{\left| {\vec T} \right|}} = \frac{1}{5}\left( { - 3\sin t\hat i + 3\cos t\hat j + 4\;\hat k} \right)\)$

Therefore Magnitude vector of the particle moving along x=3cost,y=3sint,z=4t is given by  $(\frac{{\vec T}}{{\left| {\vec T} \right|}} = \frac{1}{5}\left( { - 3\sin t\hat i + 3\cos t\hat j + 4\;\hat k} \right)\)$.

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