VITEEE 2017 Paper

Since vectors are coplanar
∴ |

a	1	1
1	b	1
1	1	c

| = 0
⇒ |

a	1	1
1−a	b−1	0
0	1−b	c−1

| = 0
[Using R2−R1 , R3−R4]
⇒ a(b - 1)(c-1)-(1 - a) {(c- 1 )-(1 -b)} = 0
⇒ a (1 - b)(1 - c) + (1 - a)( 1 - c) + (1 - a)(1 - b) = 0
⇒ (a - 1 + 1) (1 - b) (1 - c) + (1 - a) (1 - c) + (1 - a) (1 - b) = 0
⇒ (1 - b) (1 - c) + (1 - a) (1 - c) + (1 - a) (1 - b) = (1 - a) (1 - b) (1 - c)
⇒

1

1−a

+

1

1−b

+

1

1−c

= 1