The moment of the force, F → = 4 i ^ + 5 j ^ − 6 k ^ at ( 2 , 0 , − 3 ) , about the point ( 2 , − 2 , − 2 ) , is given byNEET 2018

F → = 4 i ^ + 5 j ^ - 6 k ^ r → = 2 - 2 i ^ + 0 - - 2 j ^ + - 3 - - 2 k ^ = 2 j ^ - 1 k ^ r → × F → = 2 j ^ - 1 k ^ × 4 k ^ + 5 j ^ - 6 k ^ = i ^ j ^ k ^ 0 2 - 1 4 5 - 6 = - 7 i ^ - 4 j ^ - 8 k ^

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Physics - Vectors Question with Solution | TestHub

PhysicsVectorsMultiplication of vectorsEasy2 minPYQ_2018

PhysicsEasysingle choice

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 byNEET 2018

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Answer:

Solution:

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

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

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

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

Stream:NEETSubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

⏱ 2mℹ️ Source: PYQ_2018

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