Theory question 118
Vectors(a) Find the angle between the vectors a = (−3 / 4) and b = (−8 / −15). (Column vectors written top / bottom.)
(b) Given that a = (4N, 060°) and b = (3N, 120°), Find in component form, the unit vector along a − b.
Show the model answer
Model answer
(a) a · b = 24 − 60 = −36; |a| = 5, |b| = 17
cos θ = −36/85 ≈ −0.4235, θ ≈ 115.1°
(b) Using bearings, (F, θ) = F sin θ i + F cos θ j
a = 2√3i + 2j, b = (3√3/2)i − (3/2)j
a − b = (√3/2)i + (7/2)j, |a − b| = √(3/4 + 49/4) = √13
Unit vector = (√3i + 7j)/(2√13) ≈ 0.240i + 0.971j
Explanation
Find a − b first, then divide it by its own length.