QJEEM24Mae54b: JEE Main 2024 Physics - Class 11 JEEM24Mae54b Solution: Let and . Then is equal to :

Question

Verified Solution • 2025–26 Session moderate

Let

\overrightarrow{\mathrm{a}}=-5 \hat{i}+\hat{j}-3 \hat{k}, \overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}-4 \hat{k}

and

\overrightarrow{\mathrm{c}}=(((\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \hat{i}) \times \hat{i}) \times \hat{i}

. Then

\vec{c} \cdot(-\hat{i}+\hat{j}+\hat{k})

is equal to :

Accepted Answer

\begin{aligned} &amp; \vec{a}=-5 \cdot \hat{i}+\hat{j}-3 \hat{k}, \vec{b}=\hat{i}+2 \hat{j}-4 \hat{k} \\\\ &amp; \vec{c}=(((\vec{a} \times \vec{b}) \times \hat{i}) \times \hat{i}) \times \hat{i} \\\\ &amp; =(((\vec{a} \cdot \hat{i}) \vec{b}-(\vec{b} \cdot \hat{i}) \vec{a}) \times \hat{i}) \times \hat{i} \\\\ &amp; =((-5 \vec{b}-\vec{a}) \times \hat{i}) \times \hat{i}\end{aligned}

\begin{aligned} &amp; =((-11 \hat{j}+23 \hat{k}) \times \hat{i}) \times \hat{i} \\\\ &amp; = (11 \hat{k}+23 \hat{j}) \times \hat{i} \\\\ &amp; = (11 \hat{j}-23 \hat{k})\end{aligned}

\begin{aligned} &amp; \vec{c} \cdot(-\hat{i}+\hat{j}+\hat{k})=0+11-23 \\\\ &amp; =-12\end{aligned}

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