Question

Find a vector that has the same direction as 6i + 4j but that has a different magnitude.

Answer 1

6i + 4j written in component form is < 6, 4 >.

If we factor a 2 out of each component we get this,
2 < 3, 2 >

This now represents a scalar times the vector < 3, 2 >.
Let's just give it a different scalar value to find a vector in the same direction.

1 < 3, 2 > = 3i + 2j
3 < 3, 2 > = 9i + 6j
4 < 3, 2 > = 12i + 8j

So there are some other vectors going in the same direction as 6i + 4j but with different magnitudes. We can see that 3i + 2j is one of our options, ya?