Question

Q2. For the three vectors shown in figure, A+B+C = 1j. What is vector B?
B
a. Write B in component form.
b. Write B as a magnitude and a direction.
​How to take out the direction which is part b part 2.

Answer 1

Given:

A+B+C = 1j

$\begin{array}{l}\vec{A}=4 i \\\vec{C}=-2 \mathrm{f}\end{array}$

(a)  B in component form

$\begin{array}{l}\vec{A}+\vec{B}^{\prime}+\vec{c}=1 j \\4i+\vec{B}-2 j=1 j \\\vec{B}=-4 i+2 j+1_{j} \\\vec{B}=-4 i+3 j\end{array}$

(b) magnitude of B

$\begin{aligned}|\vec{B}| &=\sqrt{4^{2}+3^{2}} \\&=5\end{aligned}$

Direction of B

$\begin{aligned}\tan \theta &=\frac{4}{3} \\&=37^{\circ}\end{aligned}$