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Question
For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = - hati + hatj - hatk` find the unit vector in the direction of the vector `veca + vecb`.
Options
`1/sqrt(2) hatj`
`1/sqrt(2) hatk`
`1/sqrt(2) hatk`
`1/sqrt(2) hati + 1/sqrt(2) hatj`
MCQ
Solution
`1/sqrt(2) hati + 1/sqrt(2) hatj`
Explanation:
`veca = 2hati - hatj + 2hatk`
= `- hati + hatj - hatk`
`veca + vecb = (2hati - hatj + 2hatk) + (-hati + hatj - hatk)`
= `(2 - 1)hati + (-1 + 1)hatj + (2 - 1)hatk`
= `hati + 0 * hatj + hatk = hati + hatk`
= `+veca + vecb| = sqrt(1^2 + 1^2) = sqrt(2)`
∴ Unit vector in the direction on of = `1/|veca + vecb| (veca + vecb) = 1/sqrt(2) (hati + hatj) = 1/sqrt(2)hati + 1/sqrt(2)hatj`
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