Question

The positions of three particles a, b, and c in a 2-D Cartesian coordinate system are given by the coordinates (3, 2), (-4, 3), and (5, -2) respectively. (a) Find the position vectors of each of the particles ~ra, ~rb , and ~rc respectively in unit vector notation along with their magnitudes. (b) If R~ is the resultant of the three vectors, then find out the magnitude and direction of the resultant vector R~ with respect to the positive x-axis. (c) Calculate the angle between the resultant vector R~ and the position vector of Particle c, ~rc.

Answer 1

a)

$\vec r_a=3\vec i+2\vec j,$

$\vec r_b=-4\vec i+3\vec j,$

$\vec r_c=5\vec i-2\vec j,$

b)

$\vec R=\vec r_a+\vec r_b+\vec r_c=4\vec i+3\vec j,$

$\theta=\arctan \frac{R_y}{R_x}=37°,$

c)

$\gamma=\arccos\frac{\vec R\cdot \vec r_c}{{|\vec R}|\cdot|{\vec r_c}|}=\arccos\frac{14}{5\sqrt{29}}=59°.$