Question
Question: If u = ax + by + cz, v = ay + bz + cx, w = ax + bx + cy then the value of \(\left| \begin{matrix} a ...
If u = ax + by + cz, v = ay + bz + cx, w = ax + bx + cy then the value of abcbcacab × xyzyzxzxy is –
A
u2 + v2 + w2 – 2uvw
B
u3 + v3 + w3 – 3uvw
C
0
D
None of these
Answer
u3 + v3 + w3 – 3uvw
Explanation
Solution
D1D2= ax+by+czbx+cy+azcx+ay+bzay+bz+cxby+cz+axcy+az+bxaz+bx+cybz+cx+aycz+ax+by
= uwvvuwwvu
= u(u2 – vw) – v(wu – v2) + w(w2 – uv)
= u3 + v3