QJEEM21Ma329e: JEE Main 2021 Physics - Class 11 JEEM21Ma329e Solution: Let a → = i ^ + j ^ + k ^ , b → and c → = j ^ − k ^ be three…

Question

Verified Solution • 2025–26 Session moderate

Let

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

and

\vec{c} = \hat{j} - \hat{k}

be three vectors such that

\vec{a} \times \vec{b} = \vec{c}

and

\vec{a} . \vec{b} = 1

. If the length of projection vector of the vector

\vec{b}

on the vector

\vec{a} \times \vec{c}

is l, then the value of 3l² is equal to _____________.

Accepted Answer

\vec{a} \times \vec{b} = \vec{c}

Take Dot with

\vec{c}

(\vec{a} \times \vec{b}) . \vec{c} = {| \vec{c} |}^{2} = 2

Projection of

\vec{b}

or

\vec{a} \times \vec{c} = l

\frac{| \vec{b} . (\vec{a} \times \vec{c}) |}{| \vec{a} \times \vec{c} |} = l

∴

l = \frac{2}{\sqrt{6}} \Rightarrow l^{2} = \frac{4}{6}

3 l^{2} = 2

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