Question

Find a vector equation and parametric equations for the line segment that joins P(2, 0, 0) Q(6, 2, 2)

Answer 1

Remember that to get vector equation you need any point that lies on to the line and a vector that goes in the same direction.

Answer 2

You could pick point P or point Q.

Answer 3

You could try\[\mathbf{r}(t)=\mathbf{P}+t(\mathbf{Q}-\mathbf{P}),\qquad0\leq t\leq1.\]Notice that if \(t=0\), then \(\mathbf{r}(t)=\mathbf{P}\), and if \(t=1\), then \(\mathbf{r}(t)=\mathbf{Q}\).

Answer 4

How do you make the letters bold @across ?

Answer 5

@across Do I just plug in the values P and Q for that formula?

Answer 6

\mathbf{}

Answer 7

just write Large before you type

Answer 8

\[\vec{r}=\large{P}\]

Answer 9

@zordoloom did you get it now ?

Answer 10

So the formula that across provided, Can I use that to find the equations?

Answer 11

first find the required parallel vector to the line
PQ=<6-2,2-0,2-0)= <4,2,2>

Answer 12

yes you can use that .

Answer 13

so, i end up with r(t)=(2,0,0)+t(4,2,-2). Is this correct?

Answer 14

r(t)=(2,0,0)+t(4,2,2 ) not -2 !!!

Answer 15

ok

Answer 16

Thanks!!

Answer 17

welcome :)