Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsMathematical Methods2 Marks
Question
Find a unit vector in the direction of the vector $3 \hat{i}+4 \hat{j}$.
✓
Answer
Given: $\quad \overrightarrow{ v }=3 \hat{ i }+4 \hat{ j }$ $\therefore \quad$ Magnitude of $\overrightarrow{ V }=|\overrightarrow{ V }|=\sqrt{3^2+4^2}=\sqrt{25}=5$ Let $\vec{V}=\hat{\alpha}|\overrightarrow{ V }|$, where $\hat{\alpha}$ is a unit vector along $\overrightarrow{ V }$ $\therefore \quad \hat{\alpha}=\frac{\overrightarrow{ V }}{|\overrightarrow{ V }|}=\frac{3 \hat{ i }+4 \hat{ j }}{5}=\frac{3}{5} \hat{ i }+\frac{4}{5} \hat{ j }$ Required unit vector is $\frac{ 3 }{5} \hat{ i }+\frac{ 4 }{5} \hat{ j }$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.