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Question
Find a vector of magnitude 20 units parallel to the vector `2hati + 5hatj + 4hatk`.
Solution
Given vector, `veca = 2hati + 5hatj + 4hatk`
`|veca| = sqrt(2^2 + 5^2 + 4^2)`
= `sqrt(4 + 25 + 16)`
= `sqrt(45)`
= `3sqrt(5)`
∴ `hata = veca/|veca|`
= `(2hati + 5hatj + 4hatk)/(3sqrt(5)`
Thus, the vector of magnitude 20 units and parallel to the `veca` is:
= `± 20. hata`
= `± (20(2hati + 5hatj + 4hatk))/(3sqrt(5))`
= `± (40hati)/(3sqrt(5)) ± (100hatj)/(3sqrt(5)) ± (80hatk)/(3sqrt(5))`
= `± (8sqrt(5))/3hati ± (20sqrt(5))/3hatj ± (16sqrt(5))/3hatk`
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