Question

Two unit vector when added give a unit vector. Then choose the correct statement.

• A. Magnitude of their difference is $\sqrt{3}$
• B. Magnitude of their difference is $1$
• C. Angle between the vectors is ${90}^{\circ }$
• D. Angle between the sum and the difference of the two vectors is ${90}^{\circ }$

Answer 1

The correct option is A Magnitude of their difference is $\sqrt{3}$

$\begin{array}{c}Lettwovectorarea,bthen\\ resul\tan tofsum={\left(a^2+b^2+2ab\cos \theta \right)}^{\frac{1}{2}}=1given\\ a=b=1\left(unitvector\right)\\ 1+1+2\cos \theta =1\\ \cos \theta =-\frac{1}{2}...........\left(1\right)\\ nowresul\tan tofdifference=magnitude\left(a-b\right)\\ R={\left(a^2+b^2-2ab\cos \theta \right)}^{\frac{1}{2}}\\ a=b=1,\\ \cos \theta =-\frac{1}{2}so\\ R={\left[1+1+1\right]}^{\frac{1}{2}}\\ =\sqrt{3}\\ Hence,\\ optionAiscorrectanswer.\end{array}$