Find the unit vector in the direction of (-5i + 12j).
Question 1 Report
Find the unit vector in the direction of (-5i + 12j).
Answer Details
To find the unit vector in the direction of a given vector, we need to divide the vector by its magnitude.
The magnitude of vector (-5i + 12j) can be found using the Pythagorean theorem as follows:
$$\left|\begin{pmatrix}-5 \\ 12 \\\end{pmatrix}\right| = \sqrt{(-5)^2 + (12)^2} = 13$$
Therefore, the unit vector in the direction of (-5i + 12j) is:
$$\frac{1}{13}\begin{pmatrix}-5 \\ 12 \\\end{pmatrix} = \frac{1}{13}(-5i + 12j)$$
So the correct option is \(\frac{1}{13}(-5i + 12j)\).
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