Question

a resultant of 2 vectors makes 30 degree with one vector and 45 degree with other find the two vectors if resultant =15

Answer 1

Hey MATE!

This must be your answer.

Hope it helps #))

Answer 2

The correct answers to the question are  $\ 10\sqrt{3}$  and $\ 15\sqrt{2}$ respectively.

CALCULATION:

Let two vectors are denoted as $\vec A \ and\ \vec B$

Let the resultant of these two vectors is denoted as $\vec R$ .

The angle made by the resultant with A is 30 degree and with B is 45 degree.

We are asked to determine these two vectors.

The angle made by $\vec R$ with $\vec A$ is 30 degree.

The component of  $\vec A$ along the direction of $\vec R$ is calculated as - $\vec A cos\theta$

Hence, the magnitude of $\vec R$ = $Acos\theta$

                                                        = A×cos30

                                                       = $A\times \frac{\sqrt{3}}{2}$

                                           ⇒       $A=\ 15\times\frac{2}{\sqrt{3}}$

                                            ⇒      $A=\ 10\sqrt{3}$  [ANS]

                                                                      

Similarly the angle made by $\vec R$ with $\vec B$ is 45 degree.

Hence, the component of B along  R is  $\R$ = $Bcos\theta$

                                                                      =  $B\times cos45$

                                                                      $=B\times \frac{1}{ \sqrt{2}}$

                                                   ⇒  $B=\ R\times \sqrt{2}$

                                                            $=\ 15\sqrt{2}$  [ans]