Chapter 1: Exercises (1.51 - 1.56)

1.51 a) Find the scalar product of the two vectors $\vec{A}$ and $\vec{B}$ given in Exercise 1.47. b) Find the angle between these two vectors.

1.52 Find the angle between each of the following pairs of vectors:
a) $\vec{A} = -2.00\hat{i} + 6.00\hat{j}$ and $\vec{B} = 2.00\hat{i} - 3.00\hat{j}$
b) $\vec{A} = 3.00\hat{i} + 5.00\hat{j}$ and $\vec{B} = 10.00\hat{i} + 6.00\hat{j}$
c) $\vec{A} = -4.00\hat{i} + 2.00\hat{j}$ and $\vec{B} = 7.00\hat{i} + 14.00\hat{j}$

1.53 Assuming a right-handed coordinate system, find the direction of the +z-axis in a) Fig. 1.15a; b) Fig. 1.15b.

1.54 For the two vectors in Fig. 1.27, a) find the magnitude and direction of the vector product $\vec{A} \times \vec{B}$; b) find the magnitude and direction of $\vec{B} \times \vec{A}$.

1.55 Find the vector product $\vec{A} \times \vec{B}$ (expressed in unit vectors) of the two vectors given in Exercise 1.47. What is the magnitude of the vector product?

1.56 For the two vectors in Fig. 1.29, a) find the magnitude and direction of the vector product $\vec{A} \times \vec{B}$; b) find the magnitude and direction of $\vec{B} \times \vec{A}$.