Find a vector that has the same direction as < -2, 4, 2> but has length 6. This probably has something to do with the magnitude and I get sqroot(24) but where do they get the 6?
In order to get a vector with different magnitude but in the same direction, find the unit vector in that direction (i.e. multiply the original vector by 1/the magnitude), then multiply the new unit vector by the magnitude that you want it to be.
so in this case you had <-2,4,2>, to get the unit vector we take the magnitude,
Then mutliply your original vector by 1 over this, which is .
we are going to then multiply our vector by this to get the unit vector but since we are going to then multiply the unit vector by 6 to get the new magnitude we can just say
Hope that helps!!!