Find the magnitude of two vectors \(\vec{a}\) and \(\vec{b}\), having the same magnitude and such that the angle between them is 60º and their scalar product is 1/2.
Answer & explanation
Correct answer: option 1
Let θ be the angle between the vectors \(\vec{a}\) and \(\vec{b}\) ,
It is given that |\(\vec{a}\)| = |\(\vec{b}\)|and (\(\vec{a}\) .\(\vec{b}\) ) = 1/2, also θ = 60º
we know that (\(\vec{a}\) .\(\vec{b}\) ) = (|\(\vec{a}\)| .|\(\vec{b}\)|)/cos(θ )
so, 1/2 = (|\(\vec{a}\)| .|\(\vec{a}\)|)/cos(60º ) (since |\(\vec{a}\)| = |\(\vec{b}\)|)
⇒|\(\vec{a}\)|2 = 1
⇒|\(\vec{a}\)| =|\(\vec{b}\)|= 1