Question

Two vectors whose magnitudes are 3x
and 5x have a resultant of magnitude 35.
If the angle of inclination of the vectors is
60°, find the value of x.​

Answer 1

Answer:

here it is

may be this will help you

Answer 2

Answer:

Given:

Magnitude of 2 vectors are given as 3x and 5x . They are inclined at 60° and have a resultant of 35 unit.

To find:

Value of x

Calculation:

As per Parallelogram Law of Vector Addition, we can say :

$\sqrt{ {(3x)}^{2} + {(5x)}^{2} + 2 \times (3x)(5x) \cos(60 \degree) } = 35$

$= > \sqrt{9 {x}^{2} + 25 {x}^{2} + (30 {x}^{2} \times \frac{1}{2} )} = 35$

$= > \sqrt{49 {x}^{2} } = 35$

$= > 49 {x}^{2} = {(35)}^{2}$

$= > {x}^{2} = \dfrac{ {(35)}^{2} }{49}$

$= > {x}^{2} = \dfrac{ {(35)}^{2} }{ {(7)}^{2} }$

$= > x = \pm\dfrac{35}{7} = \pm5$