Theory question 114
VectorsFour vectors r = αi + βj where α and β are positive constants, s = 2i − j, m = 3i + 2j and n = i + j are such that the magnitude of r is three time as s and is parallel to the vector (m − n). (a) Find the values of α and β. (b) Calculate the magnitude and direction of (r − s).
Show the model answer
Model answer
(a) m − n = 2i + j, so r = k(2i + j). |r| = 3|s| = 3√5 = k√5, so k = 3: α = 6, β = 3.
(b) r − s = 4i + 4j; magnitude 4√2 ≈ 5.66; direction 45° to the positive x-axis (bearing 045°).
Explanation
Parallel vectors are multiples of each other.