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Question
If `veca = hati +hatj + hatk, vecb = 2hati - hatj + 3hatk and vecc = hati - 2hatj + hatk` find a unit vector parallel to the vector `2veca - vecb + 3vecc`.
Solution
We have,
`veca = hati + hatj + hatk, `
`vecb = 2hati - hatj + 3hatk, `
`vecc = hati - 2hatj + 3hatk`
`= 2veca - vecb + 3vecc = 2(hati + hatj + hatk) - (2hati - hatj + 3hatk) + 3(hati - 2hatj + hatk)`
= `3hati - 3hatj + 2hatk`
= `|2veca - vecb + 3vecc|`
`= sqrt(3^2 + (-3)^2 + 2^2)`
`= sqrt(9 + 9 + 4)`
`= sqrt22`
Hence with the unit vector `2veca - vecb + 3vecc`
`(2veca - vecb + 3vecc)/|2veca - vecb + 3vecc| = ((3hati - 3hatj + 2hatk))/sqrt22`
`= 3/sqrt22hati - 3/sqrt22hatj + 2/sqrt22hatk`
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