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Question
Find a vector in the direction of vector `5hati - hatj +2hatk` which has a magnitude of 8 units.
Solution
Let, `veca = 5hati - hatj + 2hatk`
`therefore |veca| = sqrt(5^2 + (-1)^2 + 2^2)`
`= sqrt(25 + 1 + 4) `
`= sqrt30`
`therefore veca = veca/|veca| = (5hati - hatj + 2hatk)/sqrt30`
Hence, the vector in the direction of vector `5hati - hatj +2hatk`, which has a magnitude of 8 units, is given by,
`8hata = 8((5hati - hatj + 2hatk)/sqrt30)`
`= 40/sqrt30hati - 8/sqrt30hatj + 16/sqrt30hatk`
= `8((5hati - hatj + 2hatk)/sqrt30)`
= `40/sqrt30hati - 8/sqrt30hatj + 16/sqrt30hatk`
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