Let a vector \(\vec{a}\) be coplanar with vectors \(\vec{b}=2\overset{^}{i}+\overset{^}{j}+\overset{^}{k}\text{ and }\ve…

Let a vector \(\vec{a}\) be coplanar with vectors \(\vec{b}=2\overset{^}{i}+\overset{^}{j}+\overset{^}{k}\text{ and }\vec{c}=\overset{^}{i}-\overset{^}{j}+\overset{^}{k}\text{. }\)If \(\vec{a}\) is perpendicular to \(\vec{d}=3\overset{^}{i}+2\overset{^}{j}+6\overset{^}{k}\text{ and }|\vec{a}|=\sqrt{10}\) Then a possible value of \([\vec{a}\vec{b}\vec{c}]+[\vec{a}\vec{b}\vec{d}]+[\vec{a}\vec{c}\vec{d}]\) is equal to :

[JEE Main 2021, 22 Jul (Shift 2)]