Question

A man is facing North-West. He turns 90º in the clockwise direction and then 180º in the anticlockwise

direction and then another 90º in the same direction. Which direction is he facing now.​

Answer 1

Answer:

South East!

it's easy once you visualise it

Answer 2

Turning 90° in clockwise direction and then turning 180° in anticlockwise direction is the same as turning 90° in anticlockwise direction.

And from this direction, turning 90° in same direction, i.e., anticlockwise, is the same as turning 180° anticlockwisely from the initial position, i.e., Northwest.

Let me do it mathematically, even it's just logical.

Let our initial direction be 0°. We consider clockwise direction as positive and anticlockwise direction, negative.

From the question,

→ we mean turning 90° in clockwise direction as +90°

→ we mean turning 180° in anticlockwise direction as -180°

→ we mean turning 90° in anticlockwise direction as -90°

So, finally we're in the direction, 0° + 90° - 180° - 90° = - 180°, i.e., 180° anticlockwise to the direction of initial one.

Well, both 180° clockwise and anticlockwise are same!

This 180° represents the opposite direction, so the man will face in South - East direction.