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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीGiven below are two statements regarding unit vectors \( \hat{i}, \hat{j}, \hat{k} \): Statement I: The relations \( \hat{i} \times \hat{j} = \hat{k} \) and \( \hat{j} \times \hat{i} = -\hat{k} \) are both valid. Statement II: The vector product of any two mutually perpendicular unit vectors has a magnitude equal to zero. In the light of the above statements, choose the most appropriate answer from the options given below:
Correct answer · Option 3
Statement I is correct but Statement II is incorrect.
Explanation
Statement I is correct by cyclic cross-product rules and anti-commutativity. Statement II is incorrect because for perpendicular unit vectors, \( |\hat{i} \times \hat{j}| = (1)(1)\sin 90^\circ = 1 \neq 0 \).
