Scalar Multiplication
Vector AB is multiplied by scalar k to form vector AC. Adjust k by using the slider and move point B to change the magnitude and direction of vector AB. Answer the following.
1. What must happen for AC to be smaller in magnitude than AB? Larger?
2. How does changing the direction of AB change AC?
3. What happens to AC over the following intervals of k? Think in terms of magnitude and direction...
a. k < -1
b. k = -1
c. -1 < k <0
d. k = 0
4. How do the slopes of the two lines relate?
5. How do their magnitudes relate to k?
e. 0 < k <1
f. k = 1
g. k > 1