Question

part f
what does the angle comparison that you made in part e tell you about the new vector’s direction compared with that of the original vector?

Explanation:

When the angle between a vector and its scalar - multiplied vector (here, the scalar is - 4) has a difference of \(180^{\circ}\), it means the new vector ( - 4v) is in the opposite direction of the original vector (v). This is because a \(180^{\circ}\) angle between two vectors implies they are antiparallel, or pointing in exactly opposite directions.

Answer:

The new vector ( - 4v) is in the opposite direction of the original vector (v) because the angle between them is \(180^{\circ}\), indicating they are antiparallel.