Find the unit vector in the direction of the vector \(-12i + 5j\).
Answer Details
To find the unit vector in the direction of the vector \(-12i + 5j\), we need to divide the vector by its magnitude.
The magnitude of a vector with components \(a\) and \(b\) is given by the formula \(\sqrt{a^2+b^2}\).
So, the magnitude of the vector \(-12i + 5j\) is \(\sqrt{(-12)^2+5^2} = 13\).
Now, to get the unit vector, we divide each component of the vector by its magnitude:
\[\frac{-12}{13}i + \frac{5}{13}j\]
This is the unit vector in the direction of the vector \(-12i + 5j\).
Therefore, the correct option is \(\frac{-12i}{13} + \frac{5j}{13}\).