Question

If the vectors ai + j + k, i + bj + k and i + j + ck (a ≠ b ≠ c ≠ 1) are coplanar, then the value of [1] / [1 − a] + [1] / [1 − b] + [1] / [1 − c] = _________​

Answer 1

Explanation:

∣

∣

∣

∣

∣

∣

∣

a

1−a

1−a

1

b−1

0

1

0

c−1

∣

∣

∣

∣

∣

∣

∣

= 0

On expanding, we get

a (b − 1) (c − 1) − (1 − a) (c − 1) − (1 − a) (b − 1) = 0

On dividing by (1 − a) (1 − b) (1 − c), we get

[a] / [1 − a] + [1] / [1 − b] + [1] / [1 − c] = 0

⇒ [1] / [1 − a] + [1] / [1 − b] + [1] / [1 − c]

= {[1] / [1 − a]} − {[a] / [1 − a]}

= 1