Question

the magnitude of v is 5.83. the magnitude of -4v is 23.52. comparing the two magnitudes, the
$4 \times \\| \mathbf{v} \\| = 4 \times 5.83$
$= 23.32$
part e
compare the directions of v and -4v.

Explanation:

When a vector \(\mathbf{v}\) is multiplied by a scalar \(-4\), the negative sign indicates a direction change. Scalar multiplication with a negative scalar reverses the direction of the original vector. So, the direction of \(-4\mathbf{v}\) is opposite to the direction of \(\mathbf{v}\).

Answer:

The direction of \(-4\mathbf{v}\) is opposite to the direction of \(\mathbf{v}\).