LinAlg4.1.9

From Example Problems
Jump to: navigation, search

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