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Question
The unit vector perpendicular to the vectors `hat"i" - hat"j"` and `hat"i" + hat"j"` forming a right handed system is ______.
Options
`hat"k"`
`-hat"k"`
`(hat"i" - hat"j")/sqrt(2)`
`(hat"i" + hat"j")/sqrt(2)`
Solution
The unit vector perpendicular to the vectors `hat"i" - hat"j"` and `hat"i" + hat"j"` forming a right handed system is `hat"k"`.
Explanation:
Required unit vector is `((hat"i" - hat"j") xx (hat"i" + hat"j"))/|(hat"i" - hat"j") xx (hat"i" + hat"j")| = (2hat"k")/2`
= `hat"k"`.
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