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Question
Let `bara = hati - hatj, barb = hatj - hatk, barc = hatk - hati.` If `bard` is a unit vector such that `bara * bard = 0 = [(barb, barc, bard)]`, then `bard` equals ______.
Options
`+- (hati + hatj - 2hatk)/sqrt6`
`+- (hati + hatj + hatk)/sqrt3`
`+-(hati + hatj - hatk)/sqrt3`
`+- hatk`
Solution
Let `bara = hati - hatj, barb = hatj - hatk, barc = hatk - hati.` If `bard` is a unit vector such that `bara * bard = 0 = [(barb, barc, bard)]`, then `bard` equals `underlinebb(+- (hati + hatj - 2hatk)/sqrt6)`.
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