Amigrating robin flies due north with a speed of 12 m/s relative to the air. the air moves due east with a speed of 6.3 m/s relative to the ground.

consider east-west direction along X-axis  and north-south direction along Y-axis

= velocity of migrating robin relative to air = 12 j m/s

(where "j" is unit vector in Y-direction)

= velocity of air relative to ground = 6.3 i m/s

(where "i" is unit vector in X-direction)

= velocity of migrating robin relative to ground = ?

using the equation

= +

= 12 j + 6.3 i

= 6.3 i + 12 j

magnitude : sqrt((6.3)² + (12)²) = 13.6 m/s

direction : tan⁻¹(12/6.3) = 62.3 deg north of east

the components of a vector are the parts of the vectors that are to each other.

b perpendicular