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

 

Answers (1)

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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