Question

1. two vectors, each of magnitude 10 units, are inclined at an angle of 120°. find the magnitude of their resultant using the parallelogram law

Explanation:

Step1: Recall parallelogram law formula

The formula for the magnitude of the resultant $\vec{R}$ of two vectors $\vec{A}$ and $\vec{B}$ with an angle $\theta$ between them is $R = \sqrt{A^{2}+B^{2}+ 2AB\cos\theta}$.

Step2: Substitute given values

Here, $A = B=10$ units and $\theta = 120^{\circ}$, and $\cos120^{\circ}=-\frac{1}{2}$.
So, $R=\sqrt{10^{2}+10^{2}+2\times10\times10\times(-\frac{1}{2})}$.

Step3: Simplify the expression

First, calculate the terms inside the square - root:
$10^{2}=100$, so $10^{2}+10^{2}+2\times10\times10\times(-\frac{1}{2})=100 + 100-100$.
$100 + 100-100 = 100$.
Then, $R=\sqrt{100}=10$ units.

Answer:

10 units