Kinematics Question 453
Question: If three vectors along coordinate axes represent the adjacent sides of a cube of length b, then the unit vector along it’s diagonal passing through the origin will be
Options:
A) $ \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{2}} $
B) $ \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3b}} $
C) $ \hat{i}+\hat{j}+\hat{k} $
D) $ \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} $
Correct Answer: D [d] Diagonal vector $ \vec{A}=b\hat{i}+b\hat{j}+b\hat{k} $
or $ A=\sqrt{b^{2}+b^{2}+b^{2}}=\sqrt{3}b $ $ \therefore $ $ \hat{A}=\frac{{\vec{A}}}{A}=\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} $ $ \therefore $ $ \hat{A}=\frac{{\vec{A}}}{A}=\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} $
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