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(a) Show that vector adition is commutat...

(a) Show that vector adition is commutative but vector subtraction is non-commutative .
(b) For vectors `vecA=3hati-4hatj+5hatk and vecB=hati-hatj-hatk`, calculate the value of `(vecA+vecB)xx(vecA-vecB)`

Text Solution

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(b) `vecA+vecB=(3hati-4hatj+5hatk)+(hati-hatj-hatk)`
`=4hati-5hatj+4hatk`
`vecA-vecB=(3hati-4hatj+5hatk)-(hati-hatj-hatk)`
`=2hati-3hatj+6hatk`
`(vecA+vecB)xx(vecA-vecB)=|(hati,hatj,hatk),(4,-5,4),(2,-3,6)|`
`=hati(-5xx6+3xx4)+hatj(4xx2-6xx4)+hatk(-3xx4+5xx2)`
`=(-30+120)hati+(8-24)hatj+(-12+10)hatk`
`= -18hati-16hatj-2hatk`
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