# How to perform algebra when working with parallel vectors.

Find $t$ if the given vectors are parallel:

$$OR = (t , t + 2)$$

$$OS = (3 , -4)$$

I easily understand the question if the vectors are perpendicular, because the dot product of perpendicular vectors is $0$, which means you can equate the vectors to $0$ and work it out that way, but I don't understand how to answer this question with parallel vectors! And it's very frustrating!

Is there a similar rule with parallel vectors that I am unaware of?

Also, my apologies for the rubbish formatting. I haven't got the hang of mathjax yet.

• Math formatting has been taken care of. – mlc May 1 '17 at 22:31

Two vectors are parallel if they have the same slope. The slope of $(x,y)$ is $\frac{y}{x}$; so it suffices to equate $$\frac{t+2}{t} = \frac{-4}{3}$$ and find $t=-\frac{6}{7}$.
The dot product of two parallel vectors is equal to the product of their magnitudes. Thus you have $3t -4(t+2) = 5\sqrt{t^2 + (t+2)^2}$. The second solution comes from the fact that the dot product of two antiparallel vectors is also equal to the product of their magnitudes.
• $v\cdot w = \|v\|\|w\|\cos \theta$ – JMJ May 1 '17 at 22:42