১.
$\hat{\mathbf{i}}+\hat{\mathbf{j}}$ এবং $\hat{\mathbf{i}}-\hat{\mathbf{k}}$ ভেক্টর দুটির মধ্যবর্তী কোণ কত?
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$30^{\circ}$
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$45^{\circ}$
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$60^{\circ}$
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$90^{\circ}$
ব্যাখ্যা
$\begin{aligned} & |\hat{i}+\hat{j}|=\sqrt{1^2+1^2}=\sqrt{2} \\ & |\hat{i}-\hat{k}|=\sqrt{1^2+(-1)^2}=\sqrt{2} \\ & (\hat{i}+\hat{j}) \cdot(\hat{i}-\hat{k})=1 \\ & \therefore \theta=\cos ^{-1}\left\{\frac{\{\hat{i}+\hat{j}) \cdot(\hat{i}-\hat{k})}{|\hat{i}+\hat{j}||\hat{i}-\hat{k}|}\right\}=\cos ^{-1}\left(\frac{1}{\sqrt{2} \sqrt{2}}\right)=60^{\circ}\end{aligned}$