Question

Let \( \overrightarrow{ P } \) and \( \overrightarrow{ Q } \) be two vectors of the same magnitude and form a rhombus whose diagonals are \( \overrightarrow{ A } \) and \( \overrightarrow{ B } \) Mark the CORRECT statement(s) : 

(A) \( \vec{P}=\frac{1}{2}(\vec{A}+\vec{B}) \) 

(B) \( \vec{Q}=\frac{1}{2}(\vec{A}-\vec{B}) \) 

(C) \( |\overrightarrow{ A }+\overrightarrow{ B }|=|\overrightarrow{ A }-\overrightarrow{ B }| \)

(D) \( \overrightarrow{ A } \cdot \overrightarrow{ B }=0 \)

Answer 1

Correct option is (C) \(|\vec A + \vec B| =|\vec A - \vec B| \)

\(\vec A. \vec B = |\vec A| |\vec B| cos\theta\)

\(\theta = 90° \)

\(\vec A. \vec B = |\vec A| |\vec B| cos90° \)

= 0

\(|\vec A + \vec B| = \sqrt{A^2 + B^2 + 2AB \,cos\theta}\)

\(|\vec A -\vec B| = \sqrt{A^2 + B^2 + 2AB \,cos(180°- \theta)}\)

\(|\vec A - \vec B| = \sqrt{A^2 + B^2 + 2AB\, cos\theta}\)

\(|\vec A - \vec B| = |\vec A + \vec B|\)