NDA 2 2024 Maths, question 54

Topic: Vectors

Q54

Let $ABCDEF$ be a regular hexagon. If $\overrightarrow{AD}=m\overrightarrow{BC}$ and $\overrightarrow{CF}=n\overrightarrow{AB}$ , then what is $mn$ equal to?

(a) $-4$ Correct answer
(b) $-2$
(c) $2$
(d) $4$

Solution.

Answer: (a) $-4$

For consecutive vertices of a regular hexagon, the long diagonal AD is twice BC in the same direction, so m=2.
The diagonal CF is twice AB in the opposite direction, so n=−2.
Thus mn=−4.
Coordinates on a unit circle confirm both orientations.