QJEEM10Ma28fe: JEE Main 2010 Physics - Class 11 JEEM10Ma28fe Solution: If the vectors a → = i ^ − j ^ + 2 k ^ , b → = 2 i ^ + 4 j ^ +…

Question

Verified Solution • 2025–26 Session moderate

If the vectors

\vec{a} = \hat{i} - \hat{j} + 2 \hat{k}, \vec{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}

and

\vec{c} = λ \hat{i} + \hat{j} + μ \hat{k}

are mutually orthogonal, then

(λ, μ)

is equal to :

Accepted Answer

Since,

\vec{a}, \vec{b}

and

\vec{c}

are mutually orthogonal

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

\Rightarrow 2 λ + 4 + μ = 0 . . . (i)

\Rightarrow λ - 1 + 2 μ = 0 . . . (i i)

On solving

(i)

and

(i i)

, we get

λ = - 3, μ = 2

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