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Question
The unit vector perpendicular to the vectors `hati - hatj and hati + hatj` is ______.
Options
`hatk`
`-hatk + hatj`
`(hati - hatj)/sqrt2`
`(hati + hatj)/sqrt2`
MCQ
Fill in the Blanks
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Solution
The unit vector perpendicular to the vectors `hati - hatj and hati + hatj` is `bbunderline(hatk)`.
Explanation:
Vector perpendicular to `veca and vecb "is" vecc = veca xx vecb`
`vecc = (hati - hatj) xx (hati + hatj)`
= `|(hati, hatj, hatk),(1, -1, 0), (1, 1, 0)|`
= `hati(0) - hatj(0) + hatk(1 + 1)`
= `2hatk`
`"Unit vector" hatc = vecc/|vecc| = (2hatk)/|2hatk|`
= `(2hatk)/2`
= `hatk`
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