First slide

Vectors

Question

The linear velocity of a rotating body is given by $v = \vec{ω} \times \vec{r}$ where $\vec{ω}$ is the angular velocity and $\vec{r}$ is the radius vector. The angular velocity of body $\vec{ω} = i - 2 j + 2 k$ and their radius vector $\vec{r}$ = 4i-3k, then $| v |$ is

Moderate

A

$\sqrt{29} units$
B

$\sqrt{31} units$
C

$\sqrt{37} units$
D

$\sqrt{41} units$

Solution

$v = \vec{ω} \times \vec{r}$ where $\vec{ω} = i - 2 j + 2 k and \vec{r} = 4 j - 3 k$
$\begin{array}{l} = |\begin{array}{rrr} i & j & k \\ 1 & - 2 & 2 \\ 0 & 4 & - 3 \end{array}| \\ = i (6 - 8) + j (0 + 3) + k (4 + 0) \\ = - 2 i + 3 j + 4 k \\ ∴ | v | = \sqrt{[(- 2)^{2} + (3)^{2} + (4)^{2}]} = \sqrt{(29)} \end{array}$

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