# Vector properties

1. Apr 19, 2014

### Prashasti

It is well known that a vector can't be divided by a vector, as a direction can't be divided by a direction. Keeping this in mind, I used the equation, v→ = u→+a→t, and wrote it as t = v→ -u→/a→. Now, isn't it wrong to write the equation like this? As , in it, a vector, that is v→ -u→ is being divided by another, (i.e. a→)?

2. Apr 19, 2014

### Hardik Batra

This shows only equation representation. Actually you can't perform any operation like dividing.

3. Apr 19, 2014

### Staff: Mentor

Consider
$$\vec v = \vec u + \vec a t\\ \vec v - \vec u = \vec a t$$

If t > 0, then the resultant of $\vec v - \vec u$ has the same direction as $\vec a$. If t < 0, then the resultant of $\vec v - \vec u$ has the opposite direction as $\vec a$.

If you know that two vectors $\vec a$ and $\vec b$ are along the same line (i.e. one equals the other multiplied by a scalar), then you can divide one by the other to get the scalar.

Otherwise, then you indeed cannot divide them.

4. Apr 19, 2014

### mathman

If you are interested in the scalar, then all you need to divide is any (non-zero) component into its corresponding component.

In fact when you are dividing one vector by another, you are in essence carrying out three divisions instead of one to get the same result.

Last edited: Apr 19, 2014