What is the linear velocity if angular velocity vector ω = 3i - 4j + k and position vector r = 5i - 6j + 6k? (a) 6i + 2j - 3k (b) -18i - 13j + 2k (c) 18i + 13j - 2k (d) 6i - 2j + 8k

Answer: (b). Linear velocity v = ω × r. v = i[(-4)(6) - (1)(-6)] - j[(3)(6) - (1)(5)] + k[(3)(-6) - (-4)(5)] = -18i - 13j + 2k So the answer is (b) -18i - 13j + 2k.

What is the linear velocity if angular velocity vector ω = 3i - 4j +… | NEET 1999 (AIPMT)

Q16NEET 1999 · AIPMTMedium

Vector (Cross) Product

What is the linear velocity if angular velocity vector $\vec{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}$ and position vector $\vec{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}$ ?

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Answer: (b)

Linear velocity $\vec{v} = \vec{\omega} \times \vec{r}$ .
$\vec{v} = \hat{i}[(-4)(6) - (1)(-6)] - \hat{j}[(3)(6) - (1)(5)] + \hat{k}[(3)(-6) - (-4)(5)]$
$= -18\hat{i} - 13\hat{j} + 2\hat{k}$
So the answer is (b) $-18\hat{i} - 13\hat{j} + 2\hat{k}$ .

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Vector (Cross) Product question from NEET 1999 (AIPMT)

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