1. ## angle between vectors

I know the formula for the angle, cos theta = the quotient of the dot product of the product of magnitudes but I am not getting the correct answer for this problem

A ship is a (1,0) on a nautical chart with due north being the positive y-axis. The ship spots a rock at position (2,4)

a) what is the vector joining the ship to the rock?

SR=<2-1,4-0> = <1,4>

b) What angle doe the vector make with due north?

I tried using the vector for due north as <0,1> and got the wrong answer

then I used <1,0> then subtracted the value from 90 for the theta in degrees and still was incorrect.

2. ## Re: angle between vectors

$\cos \theta = \dfrac{\begin{pmatrix}1 \\ 4\end{pmatrix}\cdot \begin{pmatrix}0 \\ 1\end{pmatrix} }{\left\lVert \begin{matrix}1 \\ 4\end{matrix}\right\rVert \left\lVert \begin{matrix}0 \\ 1\end{matrix}\right\rVert } = \dfrac{4}{\sqrt{17}\sqrt{1}} = \dfrac{4}{\sqrt{17}}$

Hence, $\theta = \arccos\left(\dfrac{4}{\sqrt{17}}\right) \approx 0.25\text{ rad} \approx 14.04^\circ$

Why do you think this answer is not correct?

3. ## Re: angle between vectors

because I did the magnitude wrong. I forgot to square the 4. thanks