# A particle moves along the curve x=2t^2 y=t^2-4t and z=3t-5 where t is the time.find the components of the velocity at t=1 in the direction i-3j+2k

Question
Differential equations
A particle moves along the curve $$\displaystyle{x}={2}{t}^{{2}}{y}={t}^{{2}}-{4}{t}$$ and z=3t-5 where t is the time.find the components of the velocity at t=1 in the direction i-3j+2k

2020-11-09
$$\displaystyle\frac{{\left.{d}{x}\right.}}{{\left.{d}{t}\right.}}={4}{t},\frac{{\left.{d}{y}\right.}}{{\left.{d}{t}\right.}}={2}{t}-{4},\frac{{\left.{d}{z}\right.}}{{\left.{d}{t}\right.}}={3}.\ {A}{t}\ {t}={1}:\frac{{\left.{d}{x}\right.}}{{\left.{d}{t}\right.}}={4},\frac{{\left.{d}{y}\right.}}{{\left.{d}{t}\right.}}=-{2},\frac{{\left.{d}{z}\right.}}{{\left.{d}{t}\right.}}={3}.$$
In the direction i-3j+2k the components of the velocity would be (4,6,6).

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