Question

Let A and B be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30° and 120degree respectively, find the resultant.​

Answer 1

Answer:

Given that, vector A is 10 units and it is inclined to x axis at an angle 30° and vector B is also of 10 units which is inclined to x axis at an angle 120°. [See the attached Figure].

ANGLE B/W TWO VECTORS :

$\longrightarrow\:\:\sf \theta = 120^{\circ} -30^{\circ}$

$\longrightarrow\:\:\sf \theta =90^{\circ}$

Let's find the resultant by using TRIANGLE LAW :

$\dashrightarrow\:\:\sf | \overrightarrow{R} | = \sqrt{| \overrightarrow{A} |^{2} + | \overrightarrow{B} |^{2} + 2 | \overrightarrow{A} | \overrightarrow{B} | \cos(\theta)}$

$\dashrightarrow\:\:\sf | \overrightarrow{R} | = \sqrt{( {10)}^{2} + {(10)}^{2} + 2 (10) (10) \cos( {90}^{ \circ} )}$

$\dashrightarrow\:\:\sf | \overrightarrow{R} | = \sqrt{100 + 100+ 200 \times 0}$

$\dashrightarrow\:\:\sf | \overrightarrow{R} | = \sqrt{ 200 }$

$\dashrightarrow\:\:\sf | \overrightarrow{R} | = \sqrt{ 2 \times 10 \times 10 }$

$\dashrightarrow\:\: \underline{ \boxed{\bf | \overrightarrow{R} | =10 \sqrt{2} \:units}}$