The projections of a vector on the three coordinate axis are 6,-3,2 respectively.

Question

The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are :

Accepted Answer

Let $$P\left( {{x_1},{y_1},{z_1}} \right)$$ and $$Q\left( {{x_2},{y_2},{z_2}} \right)$$ be the initial and final points of the vector whose projections on the three coordinates axes are ${6, - 3,2}$ then

$${x_2} - {x_1}, = 6;\,\,{y_2} - {y_1} =  - 3;\,\,{z_2} - {z_1} = 2$$

So that directions ratios of $$\overrightarrow {PQ} $$ are ${6, - 3,2}$

$$\therefore$$ Direction cosines of $$\overrightarrow {PQ} $$ are

$${6 \over {\sqrt {{6^2} + {{\left( { - 3} \right)}^2} + {2^2}} }},{{ - 3} \over {\sqrt {{6^2} + {{\left( { - 3} \right)}^2} + {2^2}} }},$$

$$\,\,\,\,\,\,\,\,$$ $${2 \over {\sqrt {{6^2} + {{\left( { - 3} \right)}^2} + {2^2}} }} = {6 \over 7},{{ - 3} \over 7},{2 \over 7}$$

Solutions · 1