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

Correct answer: (D) -7 i-4 j-8 widehatk. F→=4i^+5j^-6k^ r→=2-2i^+0--2j^+-3--2k^=2j^-1k^ r→×F→=2j^-1k^×4k^+5j^-6k^ = i^ j^ k^ 0 2 -1 4 5 -6 =-7i^-4j^-8k^

Q90 / 180 · NEET 2018 · Physics

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

A
$-7 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}-4 \widehat{\mathrm{k}}$
B
$-4 \hat{\mathrm{i}}-\hat{\mathrm{j}}-8 \widehat{\mathrm{k}}$
C
$-8 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-7 \hat{\mathrm{k}}$
Correct answer
D
$-7 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-8 \widehat{\mathrm{k}}$

Solution

\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}

\vec{r} = (2 - 2) \hat{i} + (0 - (- 2)) \hat{j} + (- 3 - (- 2)) \hat{k} = 2 \hat{j} - 1 \hat{k}

\vec{r} \times \vec{F} = (2 \hat{j} - 1 \hat{k}) \times (4 \hat{k} + 5 \hat{j} - 6 \hat{k})

= |\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}

Hence, the correct answer is option: 'D'.

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

Solution

Relevant Questions

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