Which of the following pairs of vectors have the same direction?

To determine which pairs of vectors have the same direction, we need to look for vectors that represent the same line in space, meaning they point in either the same direction or exactly opposite directions.

The first option consists of the vectors (3i + 2j) and (6i + 4j). To see if they share the same direction, we can check if one vector is a scalar multiple of the other. If we multiply the first vector by 2, we get:

[

2(3i + 2j) = 6i + 4j

]

This confirms that both vectors are indeed multiples of each other, meaning they have the same direction.

Analyzing the other options:

In the second pair, (1i + 1j) and (2i + 2j), we can see that the second vector is also a multiple of the first vector (multiply the first vector by 2), indicating they share the same direction as well.

The third pair consists of (4i) and (-4i). These vectors point in opposite directions along the x-axis, but they do not share the same direction.

In the fourth option, (3i +