I have this question vector a = (2,5) vector b = (-1,t)
find t when a and b are parallel.
I can't seem to figure this one out. Theres nothing in my text about how to solve this. any help is appreciated
Actually the notation of parallel vectors is not usually associated with dot product.
The dot product of two perpendicular vectors is zero.
Rather parallel vectors are scalar multiples of each other.
Therefore, their components are proportional.
That is why we have $\displaystyle \dfrac{-1}{2}=\dfrac{t}{5} .$
Plato has the easiest way here.
I think you want to use the following
$\displaystyle \displaystyle \cos \theta = \frac{a\cdot b}{\|a\|\|b\|}$
$\displaystyle \displaystyle \cos 0 = \frac{2\times -1 +5\times t}{\sqrt{29}\sqrt{1+t^2}}$
Solving this you should get
$\displaystyle \displaystyle (2t+5)^2=0\implies t = \frac{-5}{2}$