Question

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

• A. $0^o$
• B. ${90}^o$
• C. ${45}^o$
• D. ${180}^o$

Answer 1

Answer: (B)

${90}^o$

Here, $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$

$A^2+B^2+2\overrightarrow{A}.\overrightarrow{B}=A^2+B^2-2\overrightarrow{A}.\overrightarrow{B}$

$4\overrightarrow{A}.\overrightarrow{B}=0$

As dot products of two vectors is zero so the angle between them will be ${90}^o$.