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Question
Unit vector along `vec(PQ)`, where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is ______.
Options
`2hati + 3hatj - 6hatk`
`-2hati - 3hatj + 6hatk`
`(-2hati)/7 - (3hatj)/7 + (6hatk)/7`
`(2hati)/7 + (3hatj)/7 - (6hatk)/7`
Solution
Unit vector along `vec(PQ)`, where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is `underlinebb(2hati + 3hatj - 6hatk)`.
Explanation:
Given coordinates of P are (2, 1, – 1) and Q are (4, 4, – 7).
i.e., Coordinates of `vec(PQ)`
= `(4hati + 4hatj - 7hatk) - (2hati + hatj - hatk)`
= `(4hati - 2hati) + (4hatj - hatj) + (-7hatk + hatk)`
= `2hati + 3hatj - 6hatk`.
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