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A unit vector coplanar with i+j+ 2k and ...

A unit vector coplanar with `i+j+ 2k` and `i+2j+k` and perpendicular to `i+j+k` is

Text Solution

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Let `veca=vecc+vecj+2veck`
`vecb=vecc+2vecj+veck`
`vecn=veci+vecj+veck`
`vecc=xveca+yvecb` ,br> `vecc*vecn=x(veca*vecn)+y(vecb*vecn)`
`4x+4y=0`
`y=-x`
`vecc=x(veca-vecb)=x(-vecj+veck)`
...
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