Q. $\left( \overrightarrow{\mathbf{x}} - \overrightarrow{\mathbf{y}} \right) \times \left( \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right) =$……. where $\overrightarrow{\mathbf{x}},\overrightarrow{\mathbf{y}}\ \epsilon\ R^{3}$

A) $2(\overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{y}})$
B) $|\overrightarrow{\mathbf{x}}|^{2} - |{\overrightarrow{\mathbf{y}}|}^{2}$
C) $\frac{1}{2}(\overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{y}})$
D) None of these
Explanation

(a)
$\left( \overrightarrow{\mathbf{x}} - \overrightarrow{\mathbf{y}} \right) \times (\overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}})$
$= \overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{y}} - \overrightarrow{\mathbf{y}} \times \overrightarrow{\mathbf{x}} - \overrightarrow{\mathbf{y}} \times \overrightarrow{\mathbf{y}}$
$= \overrightarrow{\mathbf{0}} + \overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{y}} + \overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{y}} - \overrightarrow{\mathbf{0}}$
$= 2(\overrightarrow{\mathbf{x}} \times \overrightarrow{\mathbf{y}})$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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