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 \(y\).

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