The moment of the force, at ( 2 , 0 , - 3 ) about the point ( 2 , - 2 ,

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Q.
The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at $(2, 0, - 3)$ about the point $(2, - 2, - 2),$ is given by [2018]

1 $- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$

2 $- 4 \hat{i} - \hat{j} - 8 \hat{k}$

3 $- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$

4 $- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

Ans.
(4)

Moment of the force is,

$\vec{τ} = (\vec{r} - {\vec{r}}_{0}) \times \vec{F}$

Here, ${\vec{r}}_{0} = 2 \hat{i} - 2 \hat{j} - 2 \hat{k}$

and $\vec{r} = 2 \hat{i} + 0 \hat{j} - 3 \hat{k}$

$∴$ $\vec{r} - {\vec{r}}_{0} = (2 \hat{i} + 0 \hat{j} - 3 \hat{k}) - (2 \hat{i} - 2 \hat{j} - 2 \hat{k}) = 0 \hat{i} + 2 \hat{j} - \hat{k}$

$∴$ $\vec{τ} =$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & - 1 \\ 4 & 5 & - 6 \end{matrix} |$ $= - 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

Solution

Q.
The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at $(2, 0, - 3)$ about the point $(2, - 2, - 2),$ is given by [2018]

1 $- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$

2 $- 4 \hat{i} - \hat{j} - 8 \hat{k}$

3 $- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$

4 $- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

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Solution

Q. The moment of the force, F→=4i^+5j^-6k^ at (2,0,-3) about the point (2,-2,-2), is given by [2018]

1 -8i^-4j^-7k^

2 -4i^-j^-8k^

3 -7i^-8j^-4k^

4 -7i^-4j^-8k^

Ans. (4) Moment of the force is, τ→=(r→-r→0)×F→ Here, r→0=2i^-2j^-2k^ and r→=2i^+0j^-3k^ ∴ r→-r→0=(2i^+0j^-3k^)-(2i^-2j^-2k^)=0i^+2j^-k^ ∴ τ→=|i^j^k^02-145-6|=-7i^-4j^-8k^

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Q.
The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at $(2, 0, - 3)$ about the point $(2, - 2, - 2),$ is given by [2018]

1 $- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$

2 $- 4 \hat{i} - \hat{j} - 8 \hat{k}$

3 $- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$

4 $- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$