My first vector problem

Geometry Level 5

If [bcd]=48[b\quad c\quad d]=48 and (a×b)×(c×d)+(a×c)×(d×b)+(a×d)×(b×c)+ka=0(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 kk

Details and Assumptions

a.b.c.da.b.c.d are vectors.

[abc][a\quad b\quad c] is scalar triple product.

x×yx\times y is cross product of xx and yy.

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