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Vector Algebra question

2025 · 3 Apr · Shift 1 · Q47

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JEE Main
Mathematics
Vector Algebra
2025 · 3 Apr · Shift 1 · Q47

Vector Algebra question

2025 · 3 Apr · Shift 1 · Q47

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

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

and

\hat{d}

be a unit vector such that

\vec{a} \times \hat{d}=\vec{b} \times \hat{d}

and

\vec{c} \cdot \hat{d}=1

. If

\vec{c}

is perpendicular to

\vec{a}

, then

|3 \lambda \hat{d}+\mu \vec{c}|^2

is equal to

\underline{\hspace{2cm}}

Numerical answer

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