Question

समान दिशा वाले दो विभिन्न सदिश लिखिए।

Answer 1

मान लीजिए विभिन्न दो सदिश a = ${\displaystyle (\hat{i}+\hat{j}+\hat{k})}$, b = ${\displaystyle (2\hat{i}+2\hat{j}+2\hat{k})}$

a के दिक् cosine

l = ${\displaystyle \frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}}}$, m = ${\displaystyle \frac{1}{\sqrt{1^2+1^2+1^2}}}$

= ${\displaystyle \frac{1}{\sqrt{3}}}$, n = ${\displaystyle \frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}}}$

a के दिक् cosine = ${\displaystyle (\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}})}$

b के दिक् cosine l = ${\displaystyle \frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}},m=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}}$

= ${\displaystyle \frac{1}{\sqrt{3}},n=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}}}$

b के दिक् cosine = ${\displaystyle (\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}})}$

इस प्रकार a, b एक ही दिशा मे है। 

Answer 2

मान लीजिए,  ${\displaystyle \overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}}$   and   ${\displaystyle \overrightarrow{b}=2\hat{i}+2\hat{j}+2\hat{k}}$

दिशा ${\displaystyle \overrightarrow{a}<\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}>}$

सदिश समान दिशा

${\displaystyle \overrightarrow{b}<\frac{2}{\sqrt{12}},\frac{2}{\sqrt{12}},\frac{2}{\sqrt{12}}>}$

इसलिए ${\displaystyle \overrightarrow{a}\ne \overrightarrow{b} \text{तथा} \overrightarrow{b}}$ की दिशा समान है।