# 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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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 = $\frac{2p+q-r}{|2p+q-r|}$

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