Kunal walks 10 km North, then 6 km South, and then 3 km East. How far from the start is he now, and in which direction relative to the starting point?

Introduction / Context:Position-tracking problems reduce to adding vectors on the North–South and East–West axes, then computing the resultant distance and bearing quadrant.

Given Data / Assumptions:

• North movement: +10 km; South movement: −6 km; net North = 4 km.
• East movement: +3 km; no West movement.
• Resultant from origin: (East 3 km, North 4 km).

Concept / Approach:Compute Pythagorean distance and determine the quadrant. The pair (3, 4) is the classic 3-4-5 right triangle.

Step-by-Step Solution:Net North = 10 − 6 = 4 km.Net East = 3 km.Distance = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 km.Direction: East positive and North positive ⇒ North-East quadrant.

Verification / Alternative check:Draw a quick coordinate sketch: starting at (0,0), you end at (3,4). The straight line back to origin is 5 km, heading South-West; hence from origin to the point is North-East 5 km.

Why Other Options Are Wrong:

• 5 km West / 7 km East / 7 km West: wrong magnitude or axis.
• None of these: unnecessary, as 5 km North-East is exact.

Common Pitfalls:Subtracting incorrectly on the North–South axis or forgetting that bearing is from the start to the final point.

Final Answer:5 kilometers North-east