Question

Three vectors OA, OB and OC act from the origin O such that the coordinates of A, B and C are (2, 5),
(8, –3) and (–10, –2), respectively.
(i) Determine whether the vectors are in equilibrium.
(ii) What will be the effect of including a fourth force OD, such that D(4, – 4)? Specify clearly.
Draw and label a diagram to illustrate your answer.

Answer 1

Explanations & Calculations

$\qquad\qquad \begin{aligned} \small \vec{OA}&=\small 2i+5j\\ \small \vec{OB}&=\small 8i-3j\\ \small \vec{OC}&=\small -10i-2j \end{aligned}$

1)

• If the sum of the vectors equals zero, then all the vectors are said to be in equilibrium.

$\qquad\qquad \begin{aligned} \small \vec{OA}+\vec{OB}+\vec{OC}&=\small(2+8-10)i+(5-3-2)j\\ &=\small 0 \end{aligned}$

• Hence, they are in equilibrium.

2)

• Since the other 3 vectors are in equilibrium, the addition of such vector results in a resultant force on the system.