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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