Vector Algebra
Quadrilateral Midpoints — Scalar k
nta_pyq_2023_apr
Grade 12
Question:
$ABCD$ quadrilateral, $E,F$ midpoints of $AC,BD$. $(\overrightarrow{AB}-\overrightarrow{BC})+(\overrightarrow{AD}-\overrightarrow{DC})=k\overrightarrow{FE}$. Then $k$ is equal to
Step-by-Step Solution
Key Concept: Express all vectors in terms of position vectors. $E=\frac{A+C}{2}$, $F=\frac{B+D}{2}$. Expand LHS.
$k=-4$.
Correct Answer: 4