If and are two vectors

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

If a\mathbf{a} and b\mathbf{b} are two vectors, then (a×b)2(\mathbf{a} \times \mathbf{b})^2 is equal to (1) ∣a⋅ba⋅ab⋅bb⋅a∣\begin{vmatrix} \mathbf{a} \cdot \mathbf{b} & \mathbf{a} \cdot \mathbf{a} \\ \mathbf{b} \cdot \mathbf{b} & \mathbf{b} \cdot \mathbf{a} \end{vmatrix} (2) ∣a⋅aa⋅bb⋅ab⋅b∣\begin{vmatrix} \mathbf{a} \cdot \mathbf{a} & \mathbf{a} \cdot \mathbf{b} \\ \mathbf{b} \cdot \mathbf{a} & \mathbf{b} \cdot \mathbf{b} \end{vmatrix} (3) ∣a⋅bb⋅a∣\begin{vmatrix} \mathbf{a} \cdot \mathbf{b} \\ \mathbf{b} \cdot \mathbf{a} \end{vmatrix} (4) None of these

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