Theory question 115
VectorsThe vectors 6i + 8j and 8i − 6j are parallel to OP and OQ respectively. If the magnitude 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.
Show the model answer
Model answer
(a) |6i + 8j| = 10, so OP = 8(6i + 8j) = 48i + 64j. |8i − 6j| = 10, so OQ = 12(8i − 6j) = 96i − 72j.
(b) PQ = OQ − OP = 48i − 136j; |PQ| = √(2304 + 18496) = √20800 = 40√13.
Explanation
Scale each direction vector to the required length.