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Three vectors aî+ĵ+k̂, î+ĵ+k̂, and î+ĵ+ck̂ are coplanar, where a, b, and c are distinct and none of them is equal to 1. Find the value of (1)/(1-a)+(1)/(1-b)+(1)/(1-c).

1. 0
2. 1
3. −1
4. 2

Correct answer: 1

Solution

For (a,1,1),(1,b,1),(1,1,c) coplanar, the determinant abc - a - b - c + 2 = 0. Dividing through leads to the identity 1/(1-a) + 1/(1-b) + 1/(1-c) = 1.

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