Question

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.

Answer 1

Answer:

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

Explanation:

Given that,

The point is

$P=(-3,1,0)$

Time t = 3

Velocity $v=(5,3,-2)$

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

Using parametric equation for position

$r(t)=r_{0}+v(t)t$....(I)

at t = 3,

$P=r(t)$

Put the value into the formula

$(-3,1,0)=r_{0}+(5,3,-2)\times3$

$(-3,1,0)=r_{0}+(15,9,-6)$

$r_{0}=(-18,-8,6)$

Put the value of r₀ in equation (I)

$r(t)=(-18,-8,6)+(5,3,-2)t$

$r(t)=(-18+5t,-8+3t,6-2t)$

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