Question

HELP FAST PLEASE!
How does multiplying a vector by a scalar value of -pi/4 change the vector?
A.) The vector will change direction and increase in magnitude.
B.) The vector will change direction and decrease in magnitude.
C.) The vector will not change direction but will increase in magnitude.
D.) The vector will not change direction but will decrease in magnitude.

Answer 1

Given a scalar number $a$ and a vector v, the product between $a$ and v is a vector, with
- magnitude given by the product between the absolute value of $a$ and the magnitude of v
- direction given by the sign of $a$: if a is positive, the final vector has same direction of v; if a is negative, the final vector has opposite direction to v.


In our problem, the scalar number is $- \frac{\pi}{4} =- \frac{3.14}{4}=-0.79$. This means that the product between the vector and this number:
- has magnitude equal to $|-0.79| = 0.79$ times the magnitude of the vector
- has opposite direction with respect to the original vector (because the scalar $a$ is negative)

Therefore, the correct answer is
B.) The vector will change direction and decrease in magnitude.