Vector Algebra
Coplanarity of four points
nta_pyq_2023_jan
Grade 12
Question:
If the four points, whose position vectors are $3\hat{i}-4\hat{j}+2\hat{k}$, $\hat{i}+2\hat{j}-\hat{k}$, $-2\hat{i}-\hat{j}+3\hat{k}$ and $5\hat{i}-2\alpha\hat{j}+4\hat{k}$ are coplanar, then $\alpha$ is equal to
\frac{73}{17}
-\frac{107}{17}
-\frac{73}{17}
\frac{107}{17}
Step-by-Step Solution
Key Concept: Set the scalar triple product of the three edge vectors (relative to one vertex) equal to zero for coplanarity.
Scalar triple product determinant $= 0 \Rightarrow \alpha = 73/17$. Answer: (1)
Correct Answer: $\frac{73}{17}$