The discussion centers on determining a vector parallel to another vector, specifically the vector $\vec{r}=<5,2-t,10+4t>$, with the parallel vector identified as $\vec{a}=<0,-1,4>$. The calculation demonstrates that $\vec{r}$ can be expressed as a linear combination of $\vec{a}$, scaled by a factor of t and translated by the point (5, 2, 10). This confirms that $\vec{a}$ is indeed parallel to $\vec{r}$, as it maintains the same direction while being offset in space.
PREREQUISITESStudents of mathematics, physics enthusiasts, and anyone studying vector calculus or linear algebra will benefit from this discussion.
Drain Brain said:I wonder how my book did the calculation for this example
$\vec{r}=<5,2-t,10+4t>$ the vector parallel to it is $\vec{a}=<0,-1,4>$
can you show the workings of this example! TIA!