Question:
(a) Find the direction cosines of the vector \( \hat{i} + \hat{j} - 2\hat{k} \).
(a) Find the direction cosines of the vector \( \hat{i} + \hat{j} - 2\hat{k} \).
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Direction cosines are calculated by dividing each component by the magnitude of the vector.
Updated On: Mar 1, 2025
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Solution and Explanation
Step1:Thedirectioncosinesarecalculatedas:
\[
l=\frac{1}{\sqrt{1^2+1^2+(-2)^2}},\,m=\frac{1}{\sqrt{1^2+1^2+(-2)^2}},\,n=\frac{-2}{\sqrt{1^2+1^2+(-2)^2}}.
\]
Simplify:
\[
l=m=\frac{1}{\sqrt{6}},\,n=\frac{-2}{\sqrt{6}}.
\]
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