Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product2 Marks
Question
Write a unit vector perpendicular to $\hat{\text{i}}+\hat{\text{j}}$ and $\hat{\text{j}}+\hat{\text{k}}.$
✓
Answer
Let $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+0\hat{\text{k}};\vec{\text{b}}=0\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ $\vec{\text{a}}\times\vec{\text{b}}=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\1&1&0\\0&1&1 \end{vmatrix}$ $=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ $\Rightarrow\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\sqrt{1+1+1}$ $=\sqrt{3}$ Unit vector perpendicular to $\vec{\text{a}}$ and $\vec{\text{b}}$ is, $\frac{\vec{\text{a}}\times\vec{\text{b}}}{\big|\vec{\text{a}}\times\vec{\text{b}}\big|}=\frac{1}{\sqrt{3}}\big(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.