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3-1.Vectors
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સદીશ ${\rm{\hat i}}\,\, + \,\,{\rm{\hat j}}\,\, + \;\,\sqrt {\rm{2}} \,\,\hat k$ નો દિશાકીય $\cos ine .......$ હોય.
A
$\frac{1}{2},\,\frac{1}{2},\,1$
B
$\frac{1}{{\sqrt 2 }},\,\,\frac{1}{{\sqrt 2 }},\frac{1}{2}$
C
$\frac{1}{2},\frac{1}{2},\frac{1}{{\sqrt 2 }}$
D
$\frac{1}{{\sqrt 2 }},\,\,\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }}$
Solution
Direction cosine of $\hat{a} \hat{i}+b \hat{j}+c \hat{k}$ can be given as
$\frac{ a }{\sqrt{ a ^2+ b ^2+ c ^2}}, \frac{ b }{\sqrt{ a ^2+ b ^2+ c ^2}} \frac{ c }{\sqrt{ a ^2+ b ^2+ c ^2}}$
Thus, here we have directional cosines as
$\frac{1}{\sqrt{1^2+1^2+(\sqrt{2})^2}}, \frac{1}{\sqrt{1^2+1^2+(\sqrt{2})^2}}$ $\frac{\sqrt{2}}{\sqrt{1^2+1^2+(\sqrt{2})^2}}$
$=\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}$
Standard 11
Physics
