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Two vectors vecA and vecB are given in t...

Two vectors `vecA` and `vecB` are given in the component form as `vecA=5hati+7hatj-4hatkandvecB=6hati+3hatj+2hatk`. Find `vecA+vecB,vecB+vecA,vecA-vecB,vecB-vecA`.

Text Solution

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`vecA+vecB=(5hati+7vecj-4hatk)+(6hati+3hatj+2hatk)=11hati+10hatj-2hatk`
`vecB+vecA=(6hati+3hatj+2hatk)+(5hati+7hatj-4veck)=(6+5)hati+(3+7)hatj+(2-4)hatk=11hati+10hatj-2hatk`
`vecA-vecB=(5hati+7hatj-4hatk)-(6hati+3hatj+2hatk)=-hati+4hatj-6hatk`
`vecB-vecA=hati-4hatj+6hatk`
Note that the vectors `vecA+vecBandvecB+vecA` are same and the vectors `vecA-vecBandvecB-vecA` are opposite to each other.
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