Question

If for two vector $( \vec { A } - \vec { B } )$. The ratio of their magnitude is

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

$( \vec { A } + \vec { B } )$ is perpendicular to $( \vec { A } - \vec { B } )$ . Thus

$( \vec { A } + \vec { B } )$ .$A ^ { 2 } + \vec { B } \cdot \vec { A } - \vec { A } \cdot \vec { B } - B ^ { 2 } = 0$

Because of commutative property of dot product $\vec { A } \cdot \vec { B } = \vec { B } \cdot \vec { A }$

$\therefore$ $A = B$

Thus the ratio of magnitudes A/B = 1