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AIEEE 2009 Solved Paper

Section: Mathematics

Question : 83 of 89

Marks: +1, -0

6,-3,2

Solution:

Let

P (x_1, y_1, z_1)

and

Q (x_2, y_2, z_2)

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

\overset{\rightarrow}{P Q}

are

6,-3,2

\therefore

Direction cosines of

\overset{\rightarrow}{P Q}

are

\;\;\frac{6}{\sqrt{6^2+(-3)^2+2^2}}, \;\frac{-3}{\sqrt{6^2+(-3)^2+2^2}}

\;\;\frac{2}{\sqrt{6^2+(-3)^2+2^2}}=\;\frac{6}{7}, \;\frac{-3}{7}, \;\frac{2}{7}

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