# Let v1 = a1i + b1j + c1k; v2 = a2i + b2j + c2k; v3 = a3i + b3j + c3k. Find the solution for v1∙(v2xv3).

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### 1 Answer

We'll recall the result of cross product of two vectors:

v4 = v2xv3 = (b2*c3 - b3*c2)i + (a2*c3 - c2*a3)j + (a2*b3 - b2*a3)k

Now, we'll calculate the dot product of v1*v4:

v1*v4 = a1*(b2*c3 - b3*c2) + b1*(a2*c3 - c2*a3) + c1*(a2*b3 - b2*a3)

The requested solution for v1*(v2xv3) is:

**v1*(v2xv3) = a1*(b2*c3 - b3*c2) + b1*(a2*c3 - c2*a3) + c1*(a2*b3 - b2*a3)**