The sum of the magnitudes of two vectors is $$18$$ and the magnitude of their resultant is $$12$$. If the resultant is perpendicular to one of the vectors, then what are the magnitudes of the two vectors ?

Question

Infinity Learn · Accepted Answer

$$P+Q=18$$…..(1)and$$ $$P2+Q2+2PQcos$$⁡θ$$=(12)2=144$$.....$$(2)Further$$ Qsin⁡θ$$P+Qcos$$⁡θ$$=$$$$tan$$⁡$$90$$∘$$=$$∞or $$P+Qcos$$⁡θ$$=0$$....$$(3)From$$ eq.$$(2),$$P2$$ $$+Q2$$ $$-2P$$ x P $$=144or$$ $$Q2-P2$$ $$=744or$$ (Q+P)(Q-P) $$=144or$$ (Q$$ $$-P) $$=8$$ ...(4)Adding$$ eqs. $$(1) and (4), we have $$2$$ Q $$=26$$ or Q $$=$$ $$13$$,Now P $$=5Hence$$, the magnitudes are $$5$$ and $$13$$.

The sum of the magnitudes of two vectors is 18 and the magnitude of their resultant is 12. If the resultant is perpendicular to one of the vectors, then what are the magnitudes of the two vectors ?

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