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If the vectors \vec{a}=\hat{i}-\hat{j}+2\hat{k},\vec{b}=2\hat{i}+4\hat{j}+4\hat{k} and \vec{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k}, are mutually orthogonal, then (\lambda ,\mu )=

  • Option 1)

    ( -3, 2 )

  • Option 2)

    ( 2, -3 )

  • Option 3)

    ( -2, 3 )

  • Option 4)

    ( 3, -2 )

 

Answers (1)

As we learnt in 

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}

 

 For mutually orthogonal,

\vec{a}.\vec{b}=0

\lambda -1+2\mu =0

\vec{b}.\vec{c}=0

2\lambda +4+\mu =0

On solving

\lambda=-3,\:\mu =2


Option 1)

( -3, 2 )

This option is correct.

Option 2)

( 2, -3 )

This option is incorrect.

Option 3)

( -2, 3 )

This option is incorrect.

Option 4)

( 3, -2 )

This option is incorrect.

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Vakul

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