Mathematics

Mathematics

Problem

If two adjacent sides of two rectangles are represented by the vectors p=5a−3b\mathbf{p} = 5\mathbf{a} - 3\mathbf{b} , q=−a−2b\mathbf{q} = -\mathbf{a} - 2\mathbf{b} and r=−4a−b\mathbf{r} = -4\mathbf{a} - \mathbf{b} ; s=−a+b\mathbf{s} = -\mathbf{a} + \mathbf{b} respectively, then the angle between the vectors x=13(p+r+s)\mathbf{x} = \frac{1}{3}(\mathbf{p} + \mathbf{r} + \mathbf{s}) and y=15(r+s)\mathbf{y} = \frac{1}{5}(\mathbf{r} + \mathbf{s}) a. π−cos⁡−1(19543)\pi - \cos^{-1}\left(\frac{19}{5\sqrt{43}}\right) b. cos⁡−1(19543)\cos^{-1}\left(\frac{19}{5\sqrt{43}}\right) c. −cos⁡−1(19543)-\cos^{-1}\left(\frac{19}{5\sqrt{43}}\right) d. π−cos⁡−1(1943)\pi - \cos^{-1}\left(\frac{19}{\sqrt{43}}\right)

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