Theory question 114
VectorsThe position vectors of points P and Q are p = 2i + 3j and q = 4i − 7j respectively. Find (a) |4p − 5q|;
(b) The scalars m and n such that mp − nq ≡ 3i − 7j.
Show the model answer
Model answer
(a) 4p − 5q = (8i + 12j) − (20i − 35j) = −12i + 47j; |4p − 5q| = √(144 + 2209) = √2353 ≈ 48.5.
(b) mp − nq = (2m − 4n)i + (3m + 7n)j = 3i − 7j.
2m − 4n = 3 and 3m + 7n = −7.
Solving: 26n = −23, n = −23/26; m = −7/26.
Explanation
Compare the i and j parts separately to get two equations.