Question

If the resultant of two vectors each of magnitude 'F' is also of magnitude 'F' then the angle between them will be: (A30 (B) 60° (C) 90° 9) 120 ​

Answer 1

Answer:

Option D) 120°

Explanation:

Given :

The resultant of two vectors each of magnitude 'F' is also of magnitude 'F'.

To find :

the angle between the two vectors.

Solution :

The resultant of two vectors 'A' and 'B' is given by,

$\rm R=\sqrt{A^2+B^2+2ABcos\theta }$

where θ is the angle between vectors A and B.

Substitute,

• Magnitude of vectors, A = B = F

• Resultant, R = F

$\sf F=\sqrt{F^2+F^2+2F^2\cos \theta} \\\\ \sf F^2=2F^2+2F^2 \cos \theta \\\\ \sf F^2=2F^2(1+\cos \theta) \\\\ \sf 1=2(1+\cos \theta) \\\\ \sf 1+\cos \theta=\dfrac{1}{2} \\\\ \sf \cos \theta=\dfrac{1}{2}-1 \\\\ \sf \cos \theta=\dfrac{-1}{2} \\\\ \sf \cos \theta=\cos 120^{\circ} \\\\ \implies \bf \theta = 120^{\circ}$

Therefore, the angle between the vectors is 120°.