Vector Algebra
Collinear Points — Finding Expression
nta_pyq_2023_apr
Grade 12
Question:
Points $\alpha\hat{i}+10\hat{j}+13\hat{k}$, $6\hat{i}+11\hat{j}+11\hat{k}$, $9\hat{i}+\beta\hat{j}-8\hat{k}$ are collinear. Then $\dfrac{(19\alpha-6\beta)^2}{2}$ is equal to
Step-by-Step Solution
Key Concept: B divides AC in some ratio $k:1$. Use section formula for each coordinate to find $\alpha$ and $\beta$.
$(19\alpha-6\beta)^2=36$. $\frac{36}{2}$... answer $=36$.
Correct Answer: 1