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Multiplication with Vectors

If under the ...

Question

If under the action of a force $(4 i + j + 3 k) N$ , a particle moves from position $r_{1} = 3 i + 2 j - 6 k$ to positions $r_{2} = 14 i + 13 j + 9 k,$ then the work done will be :

50 J

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75 J

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100 J

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175 J

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Solution

The correct option is D 100 J
Here, $r_{1} = 3 i + 2 j - 6 k$ and $r_{2} = 14 i + 13 j + 9 k$
So, displacement, $(r_{2} - r_{1}) = (14 i + 13 j + 9 k) (3 i + 2 j - 6 k)$
$= 11 i + 11 j + 15 k$
Hence, work done
$= F . s$
$= (4 i + j + 3 k) . (11 i + 11 j + 15 k)$
$= 44 + 11 + 45 = 100 J$

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Similar questions

A particle moves from position vector r1=3i^+2j^-6k^ to position vector r2=14i^+13j^+9k^ under the action of force 4i^+j^ +3k^N.Find the work done.

{¯ r}_{1} = 3^i + 2^j - 6^j

{¯ r}_{2} = 14^i + 13^j + 9^k

4^j +^j + 3^k N

{\to r}_{1} = 3^i + 2^j - 6^k

{\to r}_{2} = 14^i + 13^j - 9^k

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

N

_{1} = 3^i + 2^j - 6^k

_{2} = 14^i + 13^j + 9^k

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

{\to r}_{1} = 3^i + 2^j - 6^k

{\to r}_{2} = 14^i + 13^j - 9^k

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

N

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