# 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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