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Question
Compute the magnitude of the following vector:
`veca = hati + hatj + hatk;` `vecb = 2hati - 7hatj - 3hatk`; `vecc = 1/sqrt3 hati + 1/sqrt3 hatj - 1/sqrt3 hatk`
Solution
The given vectors are:
`veca = hati + hatj + hatk; vecb = 2hati - 7hatj - 3hatk; vecc = 1/sqrt3hati + 1/sqrt3hatj - 1/sqrt3hatk`
`|a| = sqrt((1)^2 + (1)^2 + (1)^2) = sqrt3`
`|b| = sqrt((2)^2 + (-7)^2 + (-3)^2)`
= `sqrt(4 + 49 + 9)`
= `sqrt62`
We have, `vecc = 1/sqrt3hati + 1/sqrt3 hatj - 1/sqrt3 hatk`
∴ `|vecc| = sqrt((1/sqrt2)^2 + (1/sqrt3)^2 + (-1/sqrt3)^2`
`= sqrt (1/3 + 1/3 + 1/3)`
`= sqrt(3/3)`
`= sqrt1`
= 1
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