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  • Fill in the blanks: The direction cosines of the vector ( 2hat{i}+2hat{j}-hat{k} ) are _______.

Fill in the blanks:     The direction cosines of the vector \left ( 2\hat{i}+2\hat{j}-\hat{k} \right ) are _______.

Answers (1)

If l, m, and n are the direction cosines and the direction ratios of a line are a, b, and c, then we know:

\\l=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}} \\m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}\\l=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}

According to the question,

a = 2, b = 2, c = -1

Then

\sqrt{a^{2}+b^{2}+c^{2}}=\sqrt{2^{2}+2^{2}+(-1)^{2}}=3

Thus, the direction cosines are

l = 2/3, b = 2/3, c = -1/3

 

Posted by

infoexpert24

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