Vector Algebra
Coplanar Vectors — Algebraic Identity
nta_pyq_2023_apr
Grade 12
Question:
$a\hat{i}+\hat{j}+\hat{k}$, $\hat{i}+b\hat{j}+\hat{k}$, $\hat{i}+\hat{j}+c\hat{k}$ coplanar ($a,b,c\neq1$). Then $\dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c}$ is equal to
Step-by-Step Solution
Key Concept: Coplanarity determinant $=0$. $(1-a)(1-b)(1-c)-$ terms $=0$. Use algebra to show $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=1$.
Sum $=1$.
Correct Answer: 4