Question

FIGURE $P3.25$shows vectors $\overrightarrow{A}\&\overrightarrow{B}$. Find vector $\overrightarrow{C}$such that $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=\overrightarrow{0}$. Write your answer in component form.

Short answer

The vector is$\overrightarrow{C}=-10$.

Step-by-step solution

Step 1. Given information

The following diagram is given

Step 2. The vectors

The vectors are

$$\begin{gathered} \overrightarrow{A}=4\sin 30+4\cos 60 \\ =4 \\ \overrightarrow{B}=3\cos 20+3\sin 70 \\ =6 \end{gathered}$$

Therefore, the third vector is

$$\begin{gathered} \overrightarrow{C}=-(6+4) \\ =-10 \end{gathered}$$