# Linearly independent vectors involved

Geometry Level 4

Let $\vec{a}, \vec{b}, \vec{c}$ be three linearly independent vectors, then find the value of $\dfrac{[\vec{a}+2.\vec{b}-\vec{c} \quad 2.\vec{a}+\vec{b}+\vec{c} \quad 4.\vec{a}-\vec{b}+5.\vec{c} ]}{[\vec{a} \quad \vec{b} \quad \vec{c}]}$

Note : $[\vec{a} \quad \vec{b} \quad \vec{c}]$ denotes the Scalar Triple Product of $\vec{a}, \vec{b}, \ and \ \vec{c}$

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