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Problem If two adjacent sides of two rectangles are represented by the vectors p = 5 a − 3 b \mathbf{p} = 5\mathbf{a} - 3\mathbf{b} p = 5 a − 3 b q = − a − 2 b \mathbf{q} = -\mathbf{a} - 2\mathbf{b} q = − a − 2 b r = − 4 a − b \mathbf{r} = -4\mathbf{a} - \mathbf{b} r = − 4 a − b s = − a + b \mathbf{s} = -\mathbf{a} + \mathbf{b} s = − a + b x = 1 3 ( p + r + s ) \mathbf{x} = \frac{1}{3}(\mathbf{p} + \mathbf{r} + \mathbf{s}) x = 3 1 ( p + r + s ) y = 1 5 ( r + s ) \mathbf{y} = \frac{1}{5}(\mathbf{r} + \mathbf{s}) y = 5 1 ( r + s ) π − cos − 1 ( 19 5 43 ) \pi - \cos^{-1}\left(\frac{19}{5\sqrt{43}}\right) π − cos − 1 ( 5 43 19 ) cos − 1 ( 19 5 43 ) \cos^{-1}\left(\frac{19}{5\sqrt{43}}\right) cos − 1 ( 5 43 19 ) − cos − 1 ( 19 5 43 ) -\cos^{-1}\left(\frac{19}{5\sqrt{43}}\right) − cos − 1 ( 5 43 19 ) π − cos − 1 ( 19 43 ) \pi - \cos^{-1}\left(\frac{19}{\sqrt{43}}\right) π − cos − 1 ( 43 19 ) Browse the problem library