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 $y$ .