Thread: Vectors: Finding coefficients to scalars with given vectors.

1. Vectors: Finding coefficients to scalars with given vectors.

The problem gives three vectors: a=<4,3>, b=<4,-1>, and c=<6,2>.
Using the equation c=sa+tb, with s and t as scalars, I'm supposed to find the exact values of s and t. However, I am clueless on how to solve this using a method that doesn't involve random guessing. The second scalar has thrown off my train of thought.

Using what the problem has provided, I rewrote the equation to:
<6,2> = s<4,3> + t<3,-1> and using the vector multiplication and addition properties I got:

<6,2> = <4s + 3t, 3s - t> and that's where I got stumped. Am I on the right track or am I'm not doing this right?

2. Yes, you're almost there.

So now you have two equations in two unknowns:

$\displaystyle 4s + 3t = 6$ and $\displaystyle 3s - t = 2$.

Solve them simultaneously.

3. Well I feel stupid for mixing up the numbers in my work with the given varibles, but thanks for showing how to finish the rest of the problem.