Question

vector a is 7.5 units long at a 54° angle with respect to the positive x - axis. vector b is 14.3 units long at an angle of 218°. determine the difference between the vectors, c = a - b in terms of magnitude.
your answer:
answer
units

Explanation:

Step1: Find x - components of vectors

$A_x = 7.5\cos(54^{\circ})\approx4.41$
$B_x = 14.3\cos(218^{\circ})\approx - 11.27$
$C_x=A_x - B_x\approx4.41-(-11.27) = 15.68$

Step2: Find y - components of vectors

$A_y = 7.5\sin(54^{\circ})\approx6.08$
$B_y = 14.3\sin(218^{\circ})\approx - 8.81$
$C_y=A_y - B_y\approx6.08-(-8.81)=14.89$

Step3: Calculate magnitude of vector C

$|C|=\sqrt{C_x^{2}+C_y^{2}}=\sqrt{(15.68)^{2}+(14.89)^{2}}\approx21.6$

Answer:

21.6