Question

Two equal vectors each of magnitude 20 unit inclined with an angle 120° The magnitude of their resultant is ​

Answer 1

Answer:

• Magnitude of their Resultant is 20 units .

Explanation:

According to the Question

It is given that

• Two equal vectors each of magnitude 20unit inclined with an angle 120°

We have to calculate the magnitude of their resultant .

For calculating the magnitude of their resultant

We will apply here formula $\bf\bullet\; R = \sqrt{A^2 + B^2 + 2ABcos\theta}$

Where

θ = 120°

Magnitude of each vectors are equal .

So by putting the value we get

$\dashrightarrow\bf\; R = \sqrt{20^2 + 20^2 + 2\times20\times20\times\cos120^{\circ}} \\\\\\\dashrightarrow\bf\; R =\sqrt{400+400+2\times400\times\cos120^{\circ}} \\\\\\\dashrightarrow\bf\; R = \sqrt{800+800\times(-0.5)} \\\\\\\dashrightarrow\bf\; R = \sqrt{800-400} \\\\\\\dashrightarrow\bf\; R = \sqrt{400} \\\\\\\dashrightarrow\bf\; R = 20\; units\\\\\boxed{\sf{Hence,\; the \; magnitude\; of \; their \; resultant\; is \; 20 \; units}}}$

Answer 2

Answer:

Given :-

• Two equal vectors each of magnitude 20 unit inclined with an angle of 120°.

To Find :-

• What is the magnitude of their resultant.

Formula Used :-

$\longrightarrow \sf\boxed{\bold{\pink{R^2 =\: A^2 + B^2 + 2AB\: cos\theta}}}$

Solution :-

Given :

$\bullet$ The two equal vectors each of magnitude 20 unit inclined with an angle of 120°.

According to the question by using the formula we get,

$\dashrightarrow \sf R^2 =\: A^2 + B^2 + 2AB\: cos\theta$

$\dashrightarrow \bf R =\: \sqrt{A^2 + B^2 + 2AB\: cos\theta}$

We have :

• $\sf \theta$ = 120°

$\dashrightarrow \sf R =\: \sqrt{(20)^2 + (20)^2 + 2(20)(20) \times cos\: 120^{\circ}}$

Again, as we know that :

• cos 120° = - ½

$\small \dashrightarrow \sf R =\: \sqrt{(20 \times 20) + (20 \times 20) + 2(400) \times \bigg(- \dfrac{1}{2}\bigg)}$

$\dashrightarrow \sf R =\: \sqrt{400 + 400 + 2 \times 400 \times (- 0.5)}$

$\dashrightarrow \sf R =\: \sqrt{800 + 800 \times (- 0.5)}$

$\dashrightarrow \sf R =\: \sqrt{800 - 400}$

$\dashrightarrow \sf R =\: \sqrt{400}$

$\dashrightarrow \sf R =\: \sqrt{\underline{20 \times 20}}$

$\dashrightarrow \sf\bold{\red{R =\: 20\: units}}$

$\therefore$ The magnitude of their resultant is 20 units .

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