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Vector Algebra question

2024 · 31 Jan · Shift 2 · Q51

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JEE Main
Mathematics
Vector Algebra
2024 · 31 Jan · Shift 2 · Q51

Vector Algebra question

2024 · 31 Jan · Shift 2 · Q51

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

\vec{a}=3 \hat{i}+2 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}-\hat{j}+3 \hat{k}

and

\vec{c}

be a vector such that

(\vec{a}+\vec{b}) \times \vec{c}=2(\vec{a} \times \vec{b})+24 \hat{j}-6 \hat{k}

and

(\vec{a}-\vec{b}+\hat{i}) \cdot \vec{c}=-3

. Then

|\vec{c}|^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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