Vector Algebra
Coplanar Vectors with Constraint — Sum
nta_pyq_2023_apr
Grade 12
Question:
$S$ = set of $(\lambda,\mu)$ for which $\lambda\hat{i}-\hat{j}+\hat{k}$, $\hat{i}+2\hat{j}+\mu\hat{k}$, $3\hat{i}-4\hat{j}+5\hat{k}$ coplanar, $\lambda-\mu=5$. Then $\sum_{S}80(\lambda^2+\mu^2)$ is equal to
Step-by-Step Solution
Key Concept: Coplanarity determinant $=0$ gives one equation in $\lambda,\mu$. Combined with $\lambda-\mu=5$, solve for pairs.
$2290$.
Correct Answer: 3