Question

What is the value of linear velocity, if angular velocity is $3 \hat i - 4 \hat j + \hat k$ and distance from the centre is $5 \hat i - 6 \hat j + 6 \hat k$ ?

• A. $6 \hat i + 6 \hat j - 8 \hat k$
• 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 1

Answer: (B)

$-18 \hat i - 13 \hat j + 2 \hat k$

Answer 2

Linear vector $v = \omega \times r$
Given, $\omega = 3 \hat i - 4 \hat j + \hat k \ \ and \ \ r = 5 \hat i - 6 \hat j + 6 \hat k$
$\therefore v = \begin{vmatrix} \hat i & \hat j & \hat k \\\ 3 & -4 & 1 \\\ 5 & -6 & 6 \\\ \end{vmatrix}$
$=\hat i (-24 + 6) - \hat j (18 - 5) + \hat k (-18 + 20)$
$= -18 \hat i - 13 \hat j + 2 \hat k$