# If $\left | \vec{a} \right |=\left | \vec{b} \right |, then (\vec{a}+\vec{b}).(\vec{a}-\vec{b}) \:is$ Option 1) Positive Option 2) Negative Option 3) Zero Option 4) None

As we learnt

Scalar Product of two vectors -

$\vec{a}.\vec{b}> 0 \:an\: acute\: angle$

$\vec{a}.\vec{b}< 0 \:an\: obtuse\: angle$

$\vec{a}.\vec{b}= 0 \:a\:right\: angle$

- wherein

$\Theta$  is the angle between the vectors $\vec{a}\:and\:\vec{b}$

$\left | \vec{a} \right |=\left | \vec{b} \right |$

$\left ( \vec{a}+\vec{b} \right ).\left ( \vec{a}-\vec{b} \right )=\vec{a}.\vec{a}-\vec{a}\vec{b}+\vec{b}.\vec{a}-\vec{b}.\vec{b}$

$\left | \vec{a} \right |^{2}-\left | \vec{b} \right |^{2}$          $\left [ \because \left | a \right | \right=\left | b \right | ]$

=  0

Option 1)

Positive

Incorrect Option

Option 2)

Negative

Incorrect Option

Option 3)

Zero

Correct Option

Option 4)

None

Incorrect Option

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