Question about vector coordinates

[homeworkhelpls]

Homework Statement

Find C position vector

Relevant Equations

none

here i found AB to be (-3, 2) and then i thought to do 2/5 multiplied by AB to find AC, however this is incorrect and instead i would have to involve the origin. Why and how can i involve the origin?

 

[berkeman]

The problem statement in combination with your attempt are confusing for me. Can you upload a drawing of this line please? Thanks.

 

[vela]

here i found AB to be (-3, 2) and then i thought to do 5/2 multiplied by AB to find AC

I think AB here is supposed to be the length of the line segment connecting points A and B. It's not the vector $\mathbf{b}-\mathbf{a}$, though it is related. And I think you meant you multiplied by 2/5, not 5/2. Or at least that would somewhat make sense.

Anyways, draw a sketch. I think it'll help you understand what the problem is asking for.

 

[FactChecker]

Do you know how to calculate a weighted average of vectors $a$ and $b$ so that $a$ gets 3/5 of the weight and $b$ gets 2/5? Would that point be on the AB line? How do the lengths of the AC and CB relate to the weights of the average?

 

[pasmith]

Consider $\mathbf{x}(t) = (1-t)\mathbf{a} + t\mathbf{b}$ for $0 \leq t \leq 1$