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}} $

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Answer:

Correct Answer: D

Solution:

[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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