Fast ! 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.

Given a scalar number  and a vector v, the product between  and v is a vector, with
- magnitude given by the product between the absolute value of  and the magnitude of v
- direction given by the sign of : 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 . This means that the product between the vector and this number:
- has magnitude equal to  times the magnitude of the vector
- has opposite direction with respect to the original vector (because the scalar  is negative)

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