How does multiplying a vector by a scalar value of -π/4 change the vector?
Mathematics · Middle School · Thu Feb 04 2021
Answered on
Multiplying a vector by a scalar value, such as -π/4, scales the vector by that factor and can also change its direction, depending on the sign of the scalar.
When you multiply a vector by -π/4, two things happen:
1. The magnitude (or length) of the vector is scaled by the factor π/4. This means that the new vector will be π/4 times as long as the original vector.
2. The direction of the vector is reversed because of the negative sign in -π/4. If the original vector pointed in a certain direction, the new vector will point in the exact opposite direction.
To visualize this with a simple example, consider a two-dimensional vector (a, b) being multiplied by -π/4. The resulting vector will be (-π/4 * a, -π/4 * b). If (a, b) pointed up and to the right, the new vector will point down and to the left after multiplication, and it will be π/4 times as long as the original vector.