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A particle passes through the point P=(−3,1,0)P=(−3,1,0) at time t=3t=3, moving with constant velocity v⃗ =⟨5,3,−2⟩v→=⟨5,3,−2⟩. Find a parametric equation for the position of the particle in terms of the parameter tt.

Respuesta :

Answer:

The parametric equation for the position of the particle is [tex](-18+5t,-8+3t,6-2t)[/tex].

Explanation:

Given that,

The point is

[tex]P=(-3,1,0)[/tex]

Time t = 3

Velocity [tex]v=(5,3,-2)[/tex]

We need to calculate the parametric equation for the position of the particle

Using parametric equation for position

[tex]r(t)=r_{0}+v(t)t[/tex]....(I)

at t = 3,

[tex]P=r(t)[/tex]

Put the value into the formula

[tex](-3,1,0)=r_{0}+(5,3,-2)\times3[/tex]

[tex](-3,1,0)=r_{0}+(15,9,-6)[/tex]

[tex]r_{0}=(-18,-8,6)[/tex]

Put the value of r₀ in equation (I)

[tex]r(t)=(-18,-8,6)+(5,3,-2)t[/tex]

[tex]r(t)=(-18+5t,-8+3t,6-2t)[/tex]

Hence, The parametric equation for the position of the particle is [tex](-18+5t,-8+3t,6-2t)[/tex].

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