Question

Two vectors, each of magnitude A have a resultant
of same magnitude A. The angle between the two
vectors is
(1) 30°
(2)60°
(3)120°
(4)150°​
please tell me the method to solve

Answer 1

Given :-

• Two vectors having same magnitude A have a resultant with the same magnitude of A

To find :-

• Angle between the two vectors

Formulae used :-

• Formula for the resultant of two vectors

$\orange{\bigstar}\boxed{\sf{R^2=\sqrt{M^2+N^2+2\;MN\;cos\;\theta}}}$

(where R is the magnitude of resultant of two vectors M and N , and θ is the angle between vectors M and N)

Solution :-

↦Let, two vectors be M and N having a magnitude of A

and

↦Let, their resultant be R with the same magnitude A

then

Using formula for resultant of two vectors

$\\\implies\sf{R=\sqrt{M^2+N^2+2\;MN\;cos\;\theta}}\\\\\implies\sf{A=\sqrt{A^2 + A^2 + 2 (A)(A) \;\times cos\;\theta}}\\\\\implies\sf{A^2=2A^2+2A^2\times cos\;\theta}\\\\\implies\sf{A^2=2A^2(1+cos\;\theta)}\\\\\implies\sf{(1+cos\;\theta)=\dfrac{A^2}{2A^2}}\\\\\implies\sf{1+cos\;\theta=\dfrac{1}{2}}\\\\\implies\red{\sf{cos\;\theta=-\dfrac{1}{2}}}\\\\\implies\boxed{\boxed{\red{\sf{\theta=120^{\circ}}}}}$

Therefore,

The angle between two vectors will be 120° .