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1. Angles of a unit vector with the axes ●●○○○ 20 ptsA unit vector $\vec a$ makes an angle $\frac{\pi}{3}$ with $\hat i$, an angle $\frac{\pi}{4}$ with $\hat j$, and an acute angle $\theta$ with $\hat k$. Find $\theta$ in degrees, and hence find the components of $\vec a$ along $\hat i$, $\hat j$, $\hat k$, in that order. Round the second component to two decimal places.