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Let \overrightarrow{a} and \overrightarrow{b} are two vectors then \overrightarrow{a}\cdot (\overrightarrow{a}+\overrightarrow{b})-\overrightarrow{b}\cdot (\overrightarrow{b}+\overrightarrow{a})+| \overrightarrow{b} |^{2}-\left | \overrightarrow{a} \right |^{2} equals

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

3


Answers (1)

best_answer

\vec{a}\cdot (\vec{a}+\vec{b})-\vec{b}\cdot (\vec{b}+\vec{a})+\left | \vec{b} \right |^{2}-\left |\vec{a} \right |^{2}

=\vec{a}\cdot\vec{a}+\vec{a}\cdot \vec{b}-\vec{b}\cdot \vec{b}-\vec{b}\cdot \vec{a}+| \vec{b} |^{2}-\left | \vec{a} \right |^{2}

=\left | \vec{a} \right |^{2}+(\vec{a}\cdot\vec{b}-\vec{b}\cdot \vec{a})-\left | \vec{b} \right |^{2}+\left |\vec{b} \right |^{2}-\left | \vec{a} \right |^{2}

=0

Posted by

HARSH KANKARIA

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