Let a, b, c be three distinct real numbers, none equal to one. If the vectors 
and 
are coplanar, then 
is equal to
Text Solution
Verified by ExpertsD
Given that the vectors are coplanar.
That means the determinant is equal to zero.
and 
Expand the determinant along C 1 .
(a - 1) [c(b -1)-(1- c)] + 1[(1 - b) (1 - c)] = 0
c(a - 1) (b - 1) - (a - 1) (1 - c) + (1 - b) (1 - c) = 0
c(l - a) (1 - b) + (1 - a) (1 - c) + (1 - b) (1 - c) +(1 - a)(l - b)(1 - c)
=(l - a)(l - b)(1 - c)
(1 - a) (1 - b) + (1 - a) (1 - c) + (1 - b) (1 - c)
=(1 - a)(l - b)(1 - c)
Hence this is the required option.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems