Direction Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Do the vectors

(2, 4)

and

(1, 2)

point in the same direction? Explain.

1
Step 1: Check if one is a positive scalar multiple of the other: $(2, 4) = 2 \times (1, 2)$ . Yes.
2
Step 2: Both vectors point in the same direction (ratio of components is equal: $2/1 = 4/2 = 2$ ).

Answer

Yes,

(2,4)

and

(1,2)

point in the same direction.

Two vectors point in the same direction if and only if one is a positive scalar multiple of the other. They have the same angle with the x-axis (both

\arctan(2) \approx 63.4°

) but different magnitudes (

\sqrt{20}

\sqrt{5}

About Direction

The orientation of movement or facing in space, independent of speed or distance—where something points.

A vector points from the origin to the point [formula]. What angle does it make with the positive x-

Two vectors: [formula] (east) and [formula] (south). What is the angle between them?

A ship sails [formula] (30° east of north). Express this direction as a unit vector in the standard