Vector Cross Product Squared (Jee Mains)

Scalar and Vector Products

Hard

Vector Cross Product Squared

For a triangle ABC, let $\overrightarrow p = \overrightarrow {BC} ,\overrightarrow q = \overrightarrow {CA}$ and $\overrightarrow r = \overrightarrow {BA}$ . If $\left| {\overrightarrow p } \right| = 2\sqrt 3 ,\left| {\overrightarrow q } \right| = 2$ and cosθ = $\frac{1}{{\sqrt 3 }}$ , where θ is the angle between

$\overrightarrow p$ and $\overrightarrow q$ , then ${\left| {\overrightarrow p \times \left( {\overrightarrow q - 3\overrightarrow r } \right)} \right|^2} + 3{\left| {\overrightarrow r } \right|^2}$ is equal to:

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