LinAlg4.1.9

From Exampleproblems

If the position vectors of A and B are $2\bar{i}-9\bar{j}-4\bar{k},6\bar{i}-3\bar{j}+8\bar{k}\,$ respectively,find the unit vector in the direction of AB.

Given $A=2\bar{i}-9\bar{j}-4\bar{k},B=6\bar{i}-3\bar{j}+8\bar{k}\,$

$\bar{AB}=(6\bar{i}-3\bar{j}+8\bar{k})-(2\bar{i}-9\bar{j}-4\bar{k})=4\bar{i}+6\bar{j}+12\bar{k}\,$

$|\bar{AB}|=\sqrt{4^2+6^2+(12)^2}=\sqrt{196}=14\,$

Therefore,unit vector in the direction of AB is $\frac{\bar{AB}}{|AB|}=\frac{1}{14}(4\bar{i}+6\bar{j}+12\bar{k})=\frac{2}{7}\bar{i}+\frac{3}{7}\bar{j}+\frac{6}{7}\bar{k}\,$

Main Page:Linear Algebra

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