Suppose that in a certain basis B = (x,y,z), vector u is: u = 2x+3y-z. Find a unit vector with the same direction as u.
Thank you
|u| = sqrt (2+9+1) = sqrt(12) = 2 sqrt(3)
unit vector = ( 1/{2 sqt3} ) u
= (1/6) sqrt 3 (2i+3j-k)
how did you get (2+9+1)?
Thank you
To find a unit vector with the same direction as u, we need to normalize the vector u.
To normalize a vector, we need to divide each component of the vector by the magnitude of the vector.
In this case, the vector u is u = 2x + 3y - z.
To find the magnitude of u, we use the formula:
|u| = sqrt((2^2) + (3^2) + (-1^2))
= sqrt(4 + 9 + 1)
= sqrt(14)
Now, let's normalize the vector u by dividing each component by the magnitude:
û = (2/sqrt(14))x + (3/sqrt(14))y + (-1/sqrt(14))z
Therefore, the unit vector with the same direction as u is û = (2/sqrt(14))x + (3/sqrt(14))y + (-1/sqrt(14))z.