Find a vector that has the same direction as −2, 4, 6 but has length 6.

We are givem vector < −2, 4, 6 >

First we would find norm of given vector.

In order words norm is the length of given vector.

Length of given vector ||v|| = || −2, 4, 6 || =

||v|| =

Now, we need to find a vector in the same direction as given vector but length is 6.

So, dividing 6 by the length of given vector.

We get

Multiplying this value by given vector, we get

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.