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If vec c = 3vec a+4vec b and 2vec c =vec...

If `vec c = 3vec a+4vec b and 2vec c =vec a -3vec b`, show that (i) `vec c and vec a` have the same direction and `|vec c| gt |vec a|`(ii) `vec b and vec c` have opposite direction and `|vec c| gt |vec b|`

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Verified by Experts

We have ,
` vecc=3veca+4vecb and 2 vecc=veca-3vecb`
`implies 2(3veca+4vecb)=veca-3vecb`
`implies 6veca+8vecb=veca-3vecb`
`implies 5veca=-11vecb`
`implies veca=(-11)/(5)vecb and vecb=(-5)/(11)veca`
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