M1 vectors

How do i show that 2 things will collide?

i've already set the things equal to each other and i have an expression which contains t in it but i'm not sure what to do from there

Be more specific. What "things" did you set equal to each other? What expression? How many dimensions are you working in? What's your question? What things are colliding? What are you talking about?

mechanics eyyyyy.....

How did you get 499-8t?

that's a mistake it's supposed to be 400 xD mistype

How do i show that 2 things will collide?

i've already set the things equal to each other and i have an expression which contains t in it but i'm not sure what to do from there

So now you have $10t - 500 =0$ and $400 - 8t = 0$. If they both give you the same value of $t$, then they do indeed collide and at the time $t = \frac{500}{10} = \frac{400}{8}$.

the value for t should be the same on both position vectors.

Equate the expression for the first i to the second i
Equate the expression for the first j to the second j

They collide if your value for t is the same, because the position vectors are equal to each other at the same time.