Vector Algebra
Coplanar Points — Sum of Values of α
nta_pyq_2023_apr
Grade 12
Question:
Sum of all $\alpha$ for which $\hat{i}-2\hat{j}+3\hat{k}$, $2\hat{i}-3\hat{j}+4\hat{k}$, $(\alpha+1)\hat{i}+2\hat{k}$, $9\hat{i}+(\alpha-8)\hat{j}+6\hat{k}$ are coplanar, is equal to
Step-by-Step Solution
Key Concept: Set $[\overrightarrow{AB}\ \overrightarrow{AC}\ \overrightarrow{AD}]=0$. Solve quadratic in $\alpha$.
Sum of roots $=2$.
Correct Answer: 2