Question

Find a function Bold r (t )r(t) for the line passing through the points Upper P (0 comma 0 comma 0 )P(0,0,0) and Upper Q (1 comma 7 comma 6 )Q(1,7,6). Express your answer in terms of Bold ii​, Bold jj​, and Bold kk.

Answer 1

`r(t)=-ti-7tj-6tk`

Explanation:

Given the points P(0,0,0) and Q(1,7,6).

We are to determine a function r(t) for the line passing through P and Q.

To do this, we express it in the form:

`r(t)=r_0+tD,$ where:\\ r_0$ is the starting point and D is the direction vector.`

`D=P-D=<0,0,0> -<1,7,6>=<-1,-7,-6)`

Therefore:

`r(t)=<0,0,0>+t<-1,-7,-6>\\=<-t,-7t,-6t>\\$Therefore, the function for the line passing through P and Q is:$\\r(t)=-ti-7tj-6tk`