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If x and y components of a vector `vecP` have numberical values 5 and 6 respectively and that of ` vecP + vecQ` have magnitudes 10 and 9, find the magnitude of ` vecQ` |
Answer» According to the question ` varP = 5hat + 6hatj` ` and vecP + vecQ = 10 hati + 9hatj` ` Rightarrow vecQ = ( 10hati + 9hatj) - (vecP)` `= (10 hati + 9hatj) + ( -vecP)` `= 10hati + 9 hatj - 5hatj -6hatj` ` (10-5) hatj + ( 9-6) hatj` ` Rightarrow vecQ = 5hatj + 3hatj` `or |vecQ| = sqrt(5^(2) +3^(2))` ` = sqrt(25+9)` ` |vecQ| = sqrt34` Angle that ` vecQ` makes with positive x-axis , ` theta= tan^(-1) (3/5)` ` 30.96^(@)` |
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