vectors collinear or parallel?

Hi

[laTEX]$Two\hspace{0.06in}vectors\hspace{0.06in}\overrightarrow{a}\hspace{0.06in}and\hspace{0.06in}\overrightarrow{b}\hspace{0.06in}are\hspace{0.06in}parallel\hspace{0.06in}if\hspace{0.06in}\frac{a_{1}}{b_{1}}=\frac{a_{2}}{b_{2}}=\frac{a_{3}}{b_{3}}=\lambda ,\hspace{0.06in}[/laTEX][laTEX]where\hspace{0.06in}\overrightarrow{a}=a_{1}i+a_{2}j+a_{3}k\hspace{0.06in}\overrightarrow{b}=b_{1}i+b_{2}j+b_{3}k$[/laTEX]

But I have been told that we also get the same result even when the two vectors are collinear. Then, how do we know that if they are parallel or collinear? Two parallel straight lines have different y-axis intercepts if they are not collinear. What do you say? Thank you.

Regards
PG

PG,

Then, how do we know that if they are parallel or collinear?

Click to expand...

You already told us how to discern whether two vectors are parallel. If two vectors are colinear, then they are also parallel. Two vectors are colinear when both vectors are a scalar multiple of each other. You knew that, didn't you?

Ratch

Ratchit said:

PG,



You already told us how to discern whether two vectors are parallel. If two vectors are colinear, then they are also parallel. Two vectors are colinear when both vectors are a scalar multiple of each other. You knew that, didn't you?

Ratch

Click to expand...

Yes, Sir!

I had the vague idea; that's why I mentioned the straight lines. But thanks for the confirmation.

Best regards
PG