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If p = 2i + 3j, q = 5k - 3j , r = i +2k, then find the unit vector in the direction of 2p + q - r.

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2p + q - r = 2(2\(\hat i\) + 3\(\hat j\)) + (5\(\hat k\) - 3\(\hat j\)) - (\(\hat i\) + 2\(\hat k\))

 = (4\(\hat i\) - \(\hat i\)) + (6\(\hat i\) - 3\(\hat j\)) + (5\(\hat k\) - 2\(\hat k\))

 = 3\(\hat i\) + 3\(\hat j\) + 3\(\hat k\)

|2p + q - r| = |3\(\hat i\) + 3\(\hat j\) + 3\(\hat k\)| = 3|\(\hat i\) + \(\hat j\) + \(\hat k\) |

 = 3\(\sqrt{1^2+1^2+1^2}\) = 3√3

\(\therefore\) Unit vector in the direction of 2p + q - r = \(\frac{2p+q-r}{|2p+q-r|}\)

\(=\frac{3\hat i+3\hat j+3\hat k}{3\sqrt3}\) = \(\frac{\hat i+\hat j+\hat k}{\sqrt3}\)

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