# If the vectors $\dpi{100} \vec{a}=\hat{i}-\hat{j}+2\hat{k},\vec{b}=2\hat{i}+4\hat{j}+4\hat{k}$ and $\dpi{100} \vec{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k},$ are mutually orthogonal, then $\dpi{100} (\lambda ,\mu )=$ Option 1) ( -3, 2 ) Option 2) ( 2, -3 ) Option 3) ( -2, 3 ) Option 4) ( 3, -2 )

V Vakul

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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