Theory question 114
Vectors(a) Given that AB = (4, 5) and BC = (−3, 5) (column vectors), find the: (i) angle between the vectors AB and BC;
(b) P, Q, R and M are points in the OXY plane. If PQ = 2i + 8j, PR = 11i − 12j and M divides QR internally in the ratio 3 : 7, find PM.
Show the model answer
Model answer
(a) AB·BC = −12 + 25 = 13; |AB| = √41, |BC| = √34.
cos θ = 13/√1394 ≈ 0.348, θ ≈ 69.6°.
(b) QR = PR − PQ = 9i − 20j. QM = (3/10)QR = 2.7i − 6j.
PM = PQ + QM = 4.7i + 2j.
Explanation
M is 3/10 of the way from Q to R.