Moment about the point i-2j-k- of a force represented by i- 2j-k- acting through the point 2i-3j-k is

The correct option is C 3i⃗+j⃗+k⃗ Position vector #160; #160; #160; r⃗ = (2î + 3ĵ +k̂) #160; (î + 2ĵ k̂) #160; = î + ĵ +2k̂ ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Moment about ...

Question

Moment about the point $\to i + 2 \to j - \to k$ of a force represented by $\to i + 2 \to j + \to k$ acting through the point $2 i + 3 j + k$ is

3 \to i + \to j - \to k

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3 \to i - \to j + \to k

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- 3 \to i + \to j + \to k

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3 \to i + \to j + \to k

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Solution

The correct option is C $- 3 \to i + \to j + \to k$
Position vector $\to r = (2^i + 3^j +^k)$ $- (^i + 2^j -^k)$ $=^i +^j + 2^k$
Force $\to F =$ $^i + 2^j +^k$
Torque $τ = \to r \times \to F =$ $(^i +^j + 2^k) \times$ $(^i + 2^j +^k) =$ $- 3^i +^j +^k$

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Similar questions

The shortest distance between the lines $\to r = 3 \to i + 5 \to j + 7 \to k + λ (\to i + 2 \to j + \to k) a n d \to r = - \to i - \to j - \to k + μ (7 \to i - 6 \to j + \to k) i s$

Q. The unit vector which is orthogonal to the vector

\to a = 3 \to i + 2 \to j + 6 \to k

and is coplanar with the vectors

\to b = 2 \to i + \to j + \to k

and

\to c = \to i - \to j + \to k

Q. The vector equation of the plane through the point

\to i + 2 \to j - \to k

and

⊥

to the line of intersection of the plane

\to r . (3 \to i - \to j + \to k) = 1

and

\to r . (\to i + 4 \to j - 2 \to k) = 2

Q. A unit vector coplanar with

\to i + \to j + 2 \to k

and

\to i + 2 \to j + \to k

, and perpendicular to

\to i + \to j + \to k

, is

Q. If

\to r = 3 \to i + 2 \to j - 5 \to k

\to a = 2 \to i - \to j + \to k

\to b = \to i + 3 \to j - 2 \to k

and

\to c = - 2 \to i + \to j - 3 \to k

such that

\to r = λ \to a + μ \to b + ν \to c

then

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Moment about the point →i+2→j−→k of a force represented by →i+2→j+→k acting through the point 2i+3j+k is

The correct option is C −3→i+→j+→kPosition vector →r=(2^i+3^j+^k) −(^i+2^j−^k) =^i+^j+2^kForce →F= ^i+2^j+^kTorque τ=→r×→F= (^i+^j+2^k)× (^i+2^j+^k)= −3^i+^j+^k

Moment about the point $\to i + 2 \to j - \to k$ of a force represented by $\to i + 2 \to j + \to k$ acting through the point $2 i + 3 j + k$ is

The correct option is C $- 3 \to i + \to j + \to k$
Position vector $\to r = (2^i + 3^j +^k)$ $- (^i + 2^j -^k)$ $=^i +^j + 2^k$
Force $\to F =$ $^i + 2^j +^k$
Torque $τ = \to r \times \to F =$ $(^i +^j + 2^k) \times$ $(^i + 2^j +^k) =$ $- 3^i +^j +^k$