Theory question 108
VectorsGiven that p = (8 N, 030°) and q = (9 N, 150°), find, in component form, the unit vector along (p − q).
Show the model answer
Model answer
With i east and j north: p = 8 sin 30° i + 8 cos 30° j = 4i + 6.928j; q = 9 sin 150° i + 9 cos 150° j = 4.5i − 7.794j.
p − q = −0.5i + 14.722j; |p − q| = √(0.25 + 216.74) ≈ 14.731.
Unit vector = (−0.5i + 14.722j)/14.731 ≈ −0.034i + 0.999j.
Explanation
Convert bearings to components, subtract, then divide by the magnitude.