A force F -4 -5 -3 k- is acting at point r 1-2 -3 k- The torque acting about the point r 2-3 -2 -3 k- isA- ZeroB- 42 -30 -6 k-C- 42 -30 -6 k-D- 42 -30 -6 k-

The correct option is D 42î+30ĵ 6k̂F=4î 5ĵ+3k̂ r_1=î+2ĵ+3k̂ nbsp; r_2=3î 2ĵ 3k̂ r⃗=r⃗_⃗1⃗ r⃗_⃗2⃗ = 2î+4j⃗+6k̂ torque, τ⃗= F⃗×r⃗ τ⃗=(4î 5ĵ+3k̂) × ( 2î+4j⃗+6 ...

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Byju's Answer

Standard XII

Physics

Scalar and Vector Notation

A force F =4 ...

Question

A force $\to F = 4^i - 5^j + 3^k$ is acting at point $_{1} =^i + 2^j + 3^k$ . The torque acting about the point $_{2} = 3^i - 2^j - 3^k$ is

Zero

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42^i - 30^j + 6^k

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42^i + 30^j + 6^k

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42^i + 30^j - 6^k

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Solution

The correct option is D $42^i + 30^j - 6^k$
$\to F = 4^i - 5^j + 3^k$
$_{1} =^i + 2^j + 3^k$
$_{2} = 3^i - 2^j - 3^k$

$\to r =_{1} -_{2} = - 2^i + 4 \to j + 6^k$

torque, $\to τ = \to F \times \to r$
$\to τ =$ ( $4^i - 5^j + 3^k$ ) $\times (- 2^i + 4 \to j + 6^k)$
$\to τ = (12 + 30)^i + (24 + 6)^j + (10 - 16)^k = (25^i + 30^j - 6^k)$

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Similar questions

Q. A force

\to F = 4^i - 5^j + 3^k

is acting at point

_{1} =^i + 2^j + 3^k

. The torque acting about the point

_{2} = 3^i - 2^j - 3^k

Q. A force

\to F = 4^i - 5^j + 3^k

is acting a point

_{1} =^i + 2^j + 3^k

. The torque acting about a point

_{2} = 3^i - 2^j - 3^k

Q. A force

\to F = 4^i - 5^j + 3^k

is acting at a point

_{1} =^i - 2^j + 3^k

. Find the torque acting about a point

_{2} = 3^i - 2^j - 3^k

Q. A force

(4^i + 5^j - 3^k)

newton is acting at a point

^i + 2^j + 3^k

. The torque acting a point

3^i - 2^j - 3^k

A f o r c e \to F = 4^i - 5^j + 3^k i s a c t i n g a p o i n t - - \to r_1 =^i + 2^j + 3^k

. The torque acting about a point

- - \to r_1 = 3^i - 2^j - 3^k

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A force →F=4^i−5^j+3^k is acting at point →r1=^i+2^j+3^k. The torque acting about the point →r2=3^i−2^j−3^k is

The correct option is D 42^i+30^j−6^k→F=4^i−5^j+3^k →r1=^i+2^j+3^k →r2=3^i−2^j−3^k →r=→r1−→r2=−2^i+4→j+6^k torque, →τ=→F×→r →τ=(4^i−5^j+3^k) ×(−2^i+4→j+6^k) →τ=(12+30)^i+(24+6)^j+(10−16)^k=(25^i+30^j−6^k)

A force $\to F = 4^i - 5^j + 3^k$ is acting at point $_{1} =^i + 2^j + 3^k$ . The torque acting about the point $_{2} = 3^i - 2^j - 3^k$ is