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What is the vector perpendicular to both the vectors
$\hat{i}-\hat{j}$ and $\hat{\mathrm{i}} ?$
Options:
$\hat{i}-\hat{j}$ and $\hat{\mathrm{i}} ?$
Solution:
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Verified Answer
The correct answer is:
$\hat{\mathrm{k}}$
$\quad(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \times(\hat{\mathrm{j}})$
$\quad=\hat{\mathrm{i}} \times \hat{\mathrm{i}}-\hat{\mathrm{j}} \times \hat{\mathrm{j}}=\hat{\mathrm{k}}$
$\quad=\hat{\mathrm{i}} \times \hat{\mathrm{i}}-\hat{\mathrm{j}} \times \hat{\mathrm{j}}=\hat{\mathrm{k}}$
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