ভেক্টর -2î + 3ĵ এর সমান্তরাল একটি একক ভেক্টর নির্ণয় করুন?

  1. \(\frac{-2\hat{i}}{\sqrt{13}}+\frac{3\hat{j}}{\sqrt{13}}\)
  2. \(\frac{-2\hat{i}}{\sqrt{11}}+\frac{3\hat{j}}{\sqrt{11}}\)
  3. \(\frac{-2\hat{i}}{\sqrt{15}}+\frac{3\hat{j}}{\sqrt{15}}\)
  4. 1

Answer (Detailed Solution Below)

Option 1 : \(\frac{-2\hat{i}}{\sqrt{13}}+\frac{3\hat{j}}{\sqrt{13}}\)
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Detailed Solution

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অনুসৃত ধারণা:

একক ভেক্টর সমান্তরাল \(\vec{a}=\hat{a}=\frac{\vec{a}}{\left |\vec{a} \right |}\)

গণনা:

ধরুন \(\vec{a}\) = -2î + 3ĵ

\(\Rightarrow \left | \vec{a} \right |=\sqrt{(-2)^2+3^2}=\sqrt{13}\)

∴ একক ভেক্টর সমান্তরাল \(\vec{a}=\hat{a}=\frac{\vec{a}}{\left |\vec{a} \right |}\)

\(\Rightarrow \frac{1}{\sqrt{13}}(-2\hat{i}+3\hat{j})\)

\(\Rightarrow \frac{-2\hat{i}}{\sqrt{13}}+\frac{3\hat{j}}{\sqrt{13}}\)

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