Question

Three vectors A, B, and C have the following components: A_x = 5.20, A_y = 6.37; B_x = 3.92, B_y = -3.00; C_x = -2.00, C_y = 5.00.

(a) Find the x and y components of A + B + C.

x-component	units
y-component	units

(b) Find the magnitude and direction of A + B + C.

magnitude	units
direction	counterclockwise from the positive x-axis

Answer 1

(a)

we know that x component of A+B+C will be the sum of respective x components of all vectors.

So,

X component= 5.2+3.92-2

x=7.12

Similarly y component will be,

y=6.37-3+5

y=8.37

(b)

Magnitude will be

$M=\sqrt{x^{2}+y^{2}}$

$M=\sqrt{7.12^{2}+8.37^{2}}$

M=10.98

And direction will be

$\theta = \tan^{-1}\frac{y}{x}$

$\theta = \tan^{-1}\frac{8.37}{7.12}$

$\theta = 49.61$