Answer to Question #102666 in Analytic Geometry for Akinkunmi

Question

Vectors of points A and B are 2i-3j+4k and 3i-7j+12k respectively

Answer 1

Vectors of points A and B are 2i-3j+4k and 3i-7j+12k respectively. Find the length of AB and its direction cosines.

$$\bold {OA}=2\bold {i}-3\bold {j}+4\bold {k}, \bold {OB}=3\bold {i}-7\bold {j}+12\bold {k}$$

$$\bold {AB}=\bold {OB}-\bold {OA}$$

$$\bold {AB}=3\bold {i}-7\bold {j}+12\bold {k}-(2\bold {i}-3\bold {j}+4\bold {k})$$ $$\bold {AB}=\bold {i}-4\bold {j}+8\bold {k}$$

$$AB=|\bold{AB}|=\sqrt{1^2+(-4)^2+8^2}=9$$ $$AB=9$$

Direction cosines are

$${1 \over 9},\ -{4 \over 9}, \ {8 \over 9}$$