QJEEM09Mae7c3: JEE Main 2009 Mathematics - Class 12 JEEM09Mae7c3 Solution: The projections of a vector on the three coordinate axis are…

Question

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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}

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