Question

Find a unit vector that has the same direction as [-2, 4, 2] but has length 6.

Answer 1

Answer: The required unit vector would be
`\frac{-\hat{i}+2\hat{j}+1\hat{k}}{√(6)}`

Explanation:

Since we have given that

Let a be the vector which has the same direction as
`-2\hat{i}+4\hat{j}+2\hat{k}` and has length 6.

Since they are in the same direction so, both have same length i.e. magnitude.

So, the unit vector of a would be

`\hat{a}=(u)/(|u|)=\frac{-2\hat{i}+4\hat{j}+2\hat{k}}{√(-2^2+4^2+2^2)}\\\\\hat{a}=\frac{-2\hat{i}+4\hat{j}+2\hat{k}}{√(4+16+4)}\\\\\hat{a}=\frac{-2\hat{i}+4\hat{j}+2\hat{k}}{√(24)}\\\\\hat{a}=\frac{-\hat{i}+2\hat{j}+1\hat{k}}{√(6)}`

Hence, the required unit vector would be
`\frac{-\hat{i}+2\hat{j}+1\hat{k}}{√(6)}`