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If x and y components of a vector vecP h...

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`

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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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