Let $\vec{a}=\langle-1,-5\rangle$ and $\vec{b}=\langle 5,-1\rangle$. Find the angle between the vector, in degrees. Question Help: $\square$ Video Submit Question

Step 1 ：Let's define the vectors \(\vec{a}=\langle-1,-5\rangle\) and \(\vec{b}=\langle 5,-1\rangle\).

Step 2 ：We calculate the dot product of the vectors, which is \(a[0]*b[0] + a[1]*b[1] = 0\).

Step 3 ：Next, we calculate the magnitudes of the vectors. The magnitude of \(\vec{a}\) is \(\sqrt{a[0]^2 + a[1]^2} = 5.0990195135927845\), and the magnitude of \(\vec{b}\) is \(\sqrt{b[0]^2 + b[1]^2} = 5.0990195135927845\).

Step 4 ：We then calculate the angle between the vectors in radians, which is \(\cos^{-1}(\frac{dot\_product}{magnitude\_a * magnitude\_b}) = 1.5707963267948966\).

Step 5 ：Finally, we convert the angle from radians to degrees by multiplying by \(\frac{180}{\pi}\), which gives us the final answer of \(90\) degrees.