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प्रश्न
For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = -hati + hatj - hatk`, find the unit vector in the direction of the vector `veca +vecb`.
उत्तर
The given vectors are,
`veca = 2hati - hatj + 2hatk`, and `vecb = -hati + hatj - hatk`
⇒ `veca = 2hati - hatj + 2hatk`
⇒ `vecb = -hati + hatj - hatk`
`therefore veca + vecb = (2 - 1)hati + (-1 + 1)hatj + (2 - 1)hatk = 1hati + 0hatj + 1hatk = hati + hatk`
∴ `|veca + vecb| = sqrt(1^2 + 1^2) `
`= sqrt2`
Hence, the unit vector in the direction of `((veca + vecb))/(|veca + vecb|) = (hati + hatk)/sqrt2 = 1/sqrt2hati + 1/sqrt2hatk`
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