Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
The unit vector perpendicular to both vectors $\hat{i}+\hat{k}$ and $\hat{i}-\hat{k}$ is:
✓
Answer
Let the required vector be $x \hat{i}+y \hat{j}+z \hat{k}$. Then, $x^2+y^2+z^2=1$ .............(i) Also, $(x \hat{i}+y \hat{j}+z \hat{k}) \cdot(\hat{i}+\hat{k})=0$ $\Rightarrow \quad x+z=0 ........(ii)$ And $(x \hat{i}+y \hat{j}+z \hat{k}) \cdot(\hat{i}-\hat{k})=0$ $\Rightarrow x - z =0 .........(iii)$ Solving (ii) and (iii), we get $x=z=0$ $\therefore \quad$ From (i), $y^2=1 \Rightarrow y= \pm 1$ So, required vector is $\pm \hat{j}$.
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