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A(1,1,1), B(2,5,0), C(3,2,-3) and D(1,-6...

A(1,1,1), B(2,5,0), C(3,2,-3) and D(1,-6,-1) are the vertices of quadrilateral. Show that AB||CD and AB = `1/2`CD

Text Solution

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`vecA=hati+hatj+hatk`
`vecB=2hati+5hatj`
`vecC=3hati+2hatj-3hatk`
`vecD=hati-6hatj-hatk`
`vec(AB)=vecB-vecA=(2hati-hati)+(5hatj-hatj)-hatk`
`=hati+4hatj-hatk`
`vec(CD)=vecD-vecC=(hati-3hati)+(-6hatj-2hatj)-hatk+3hatk`
`-2(hati+4hatj-hatk)`
...
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