Question

If the vectors ai + j + k, i + bj + k and i + j + ck, (a, b, c ≠ 1) are coplanar, the value of (1/(1 – a)) + (1/(1 – b)) + (1/(1 – c)) is ...

Answer 1

Given

= a(b – 1)(c – 1) – (1 – a)(c – 1) + (1 – a)(1 – b) = 0 

= a(1 – b)(1 – c) + (1 – a)(1 – c) + (1 – a)(1 – b) = 0

Divide both the sides by (1 – a)(1 – b)(1 – c),

we get