Question

15. The vectors 6i+8j and 8i−6j are parallel to OP and OQ respectively. If the magnitudes of OP and OQ are 80 units and 120 units respectively, express:
(a) OP and OQ in terms of i and j;
(b) |PQ|, in the form c√k, where c and k are constants.

Accepted Answer

(a) Unit vector along 6i+8j = (6i+8j)/10 = 0.6i+0.8j. OP = 80(0.6i+0.8j) = 48i+64j.
Unit vector along 8i−6j = (8i−6j)/10 = 0.8i−0.6j. OQ = 120(0.8i−0.6j) = 96i−72j.
(b) PQ = OQ−OP = (96i−72j)−(48i+64j) = 48i−136j.
|PQ| = √(48²+136²) = √20800 = 40√13 units.

WAEC Further Mathematics 2022 Theory — Question 15

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