What is the value of linear velocity, if

What is the value of linear velocity, if \( \vec{\omega} = 3\hat{i} - 4\hat{j} + \hat{k} \) and \( \vec{r} = 5\hat{i} - 6\hat{j} + 6\hat{k} \)?

A) \( 6\hat{i} + 2\hat{j} - 3\hat{k} \)
B) \( -18\hat{i} - 13\hat{j} + 2\hat{k} \)
C) \( 4\hat{i} - 13\hat{j} + 6\hat{k} \)
D) \( 6\hat{i} - 2\hat{j} + 8\hat{k} \)

Answer: B) \( -18\hat{i} - 13\hat{j} + 2\hat{k} \)

The linear velocity \( \vec{v} \) is calculated using the cross product:

\[ \vec{v} = \vec{\omega} \times \vec{r} \]

Using determinant expansion:

\[ \vec{v} = -18\hat{i} - 13\hat{j} + 2\hat{k} \]

MCQ On Motion In Plane | Newton's Laws Of Motion | CBSE, IIT JEE, NEET, CET | Physics PYQ

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