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Vector Algebra question

2023 · 11 Apr · Shift 2 · Q37

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JEE Main
Mathematics
Vector Algebra
2023 · 11 Apr · Shift 2 · Q37

Vector Algebra question

2023 · 11 Apr · Shift 2 · Q37

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

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

and

\vec{b}=\hat{i}+\hat{j}-\hat{k}

. If

\vec{c}

is a vector such that

\vec{a} \cdot \vec{c}=11, \vec{b} \cdot(\vec{a} \times \vec{c})=27

and

\vec{b} \cdot \vec{c}=-\sqrt{3}|\vec{b}|

, then

|\vec{a} \times \vec{c}|^{2}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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