# My first vector problem

**Geometry**Level 5

If \([b\quad c\quad d]=48\) and \((a\times b)\times (c\times d)+(a\times c)\times (d\times b)+(a\times d)\times (b\times c)+ka=0\) then find value of \(k\)

**Details and Assumptions**

\(a.b.c.d\) are vectors.

\([a\quad b\quad c]\) is **scalar triple product**.

\(x\times y\) is **cross product** of \(x\) and \(y\).