# What is the moment about the point $\hat i + 2\hat j - \hat k$ of a force represented by $3\hat i + \hat k$ acting through the point $2\hat i - \hat j + 3\hat k$?

${\text{A}}{\text{. }} - 3\hat i + 11\hat j + 9\hat k$

${\text{B}}{\text{. }}3\hat i + 2\hat j + 9\hat k$

${\text{C}}{\text{. }}3\hat i + 4\hat j + 9\hat k$

${\text{D}}{\text{. }}\hat i + \hat j + \hat k$

Last updated date: 16th Mar 2023

•

Total views: 308.1k

•

Views today: 7.88k

Answer

Verified

308.1k+ views

Hint- Moment of force is given by $\vec T = \vec r{\text{ }} \times {\text{ }}\vec F$ where $\vec F$ is the force acting perpendicular to the point and r is perpendicular distance between the force acting and axis of rotation.

As it is given in the question that the force acts through the points. So, let first point be represented by vector $\vec A = \hat i + 2\hat j - \hat k$ and other point by vector $\vec B = 2\hat i - \hat j + 3\hat k$ then,

According to the rule, we calculate $\vec r$,where $\vec r$ is the resultant vector of $\vec B$ and $\vec A$ given as

$

\vec r = \vec B - \vec A \\

\Rightarrow 2\hat i - \hat j + 3\hat k - \left( {\hat i + 2\hat j - \hat k} \right) \\

\Rightarrow \hat i - 3\hat j + 4\hat k \\

$

Now, as per the question we have to find the moment of a force $\vec F = 3\hat i + \hat k$.

So, we have a formula for calculating moment of force that is Moment $\vec T = \vec r{\text{ }} \times {\text{ }}\vec F$

we will put the value of $\vec r$ and $\vec F$ in the formula, we get

$ \Rightarrow \left( {\hat i - 3\hat j + 4\hat k} \right) \times \left( {3\hat i + \hat k} \right)$

Writing the above equation in matrix form

$

\Rightarrow \left( {\begin{array}{*{20}{c}}

i&j&k \\

1&{ - 3}&4 \\

3&0&1

\end{array}} \right) \\

\Rightarrow - 3\hat i + 11\hat j + 9\hat k \\

$

Therefore moment $\vec T = - 3\hat i + 11\hat j + 9\hat k$

So, option “A” is correct.

Note- In this type of question basic concept of Moment and knowledge of vectors is required. As it is given that force is acting on a point so first find a vector $\vec r$ and after that using the cross product find moment of force $\vec T$.

As it is given in the question that the force acts through the points. So, let first point be represented by vector $\vec A = \hat i + 2\hat j - \hat k$ and other point by vector $\vec B = 2\hat i - \hat j + 3\hat k$ then,

According to the rule, we calculate $\vec r$,where $\vec r$ is the resultant vector of $\vec B$ and $\vec A$ given as

$

\vec r = \vec B - \vec A \\

\Rightarrow 2\hat i - \hat j + 3\hat k - \left( {\hat i + 2\hat j - \hat k} \right) \\

\Rightarrow \hat i - 3\hat j + 4\hat k \\

$

Now, as per the question we have to find the moment of a force $\vec F = 3\hat i + \hat k$.

So, we have a formula for calculating moment of force that is Moment $\vec T = \vec r{\text{ }} \times {\text{ }}\vec F$

we will put the value of $\vec r$ and $\vec F$ in the formula, we get

$ \Rightarrow \left( {\hat i - 3\hat j + 4\hat k} \right) \times \left( {3\hat i + \hat k} \right)$

Writing the above equation in matrix form

$

\Rightarrow \left( {\begin{array}{*{20}{c}}

i&j&k \\

1&{ - 3}&4 \\

3&0&1

\end{array}} \right) \\

\Rightarrow - 3\hat i + 11\hat j + 9\hat k \\

$

Therefore moment $\vec T = - 3\hat i + 11\hat j + 9\hat k$

So, option “A” is correct.

Note- In this type of question basic concept of Moment and knowledge of vectors is required. As it is given that force is acting on a point so first find a vector $\vec r$ and after that using the cross product find moment of force $\vec T$.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?