Question

Let the vectors PQ, QR, RS, ST, TU and UP represent the sides of a regular hexagon.

Statement I: PQ × (RS + ST) ≠ 0

Statement II: PQ × RS = 0 and PQ × ST ≠ 0

Answer 1

We have RS + ST = RT

As PQ and TR are not parallel to each other.

PQ × (RS × ST) ≠ 0

Thus, statement-I is true.

Next, since PQ and RS are not parallel, so,

PQ × RS ≠ 0

Thus, statement-II is false