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Vector Algebra question

2023 · 31 Jan · Shift 2 · Q42

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JEE Main
Mathematics
Vector Algebra
2023 · 31 Jan · Shift 2 · Q42

Vector Algebra question

2023 · 31 Jan · Shift 2 · Q42

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

\vec{a}, \vec{b}, \vec{c}

be three vectors such that

|\vec{a}|=\sqrt{31}, 4|\vec{b}|=|\vec{c}|=2

and

2(\vec{a} \times \vec{b})=3(\vec{c} \times \vec{a})

. If the angle between

\vec{b}

and

\vec{c}

is

\frac{2 \pi}{3}

, then

\left(\frac{\vec{a} \times \vec{c}}{\vec{a} \cdot \vec{b}}\right)^{2}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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