Maths. Section B1Vectors

If | a |=3| b|,|b |=2 and angle between a and b is 60o,then | a-b | i…

If |$\vec{a}$|=3|$\vec{b}|,|\vec{b}$|=2 and angle between $\vec{a}$ and $\vec{b}$ is 60^o,then |$\vec{a}-\vec{b}$| is equal to:

Answer & explanation

Correct answer: option 2

$|\vec{a}|=3|\vec{b}|,|\vec{b}|=2$ i.e. $|\vec{a}| =3×2=6$

let θ be angle between $\vec{a}\, \And\, \vec{b}$ then θ = 60^o

$|\vec{a}-\vec{b}|=\sqrt{|\vec{a}|^2+|\vec{b}|^2-2\vec{a}\vec{b}}$

$=\sqrt{36+4-2×\frac{1}{2}×2}=\sqrt{40-12}=\sqrt{28}=2\sqrt{7}$

So option 2 is correct.