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Find the workdone if a particle moves fr...

Find the workdone if a particle moves from position `vec(r )_(1)=(2hat(j)+hat(j)-3hat(k))` to a position `vec(r )_(2)=(4hat(i)+6hat(j)-7hat(k))` under the effect of force `vec(F)=(3hat(i)+2hat(j)+4hat(k))N`.

Text Solution

Verified by Experts

`vec(r) = 7 hat(i) + 4 hat(j) - 2 hat(k)`
`vec(F) = 4 hat(i) - 3 hat(j) + 5 hat(k)`
Torque, `vec(tau) = vec(r) xx vec(F)`
`vec(tau) = |(hat(i),hat(j),hat(k)),(7,4,-2),(4,-3,5)|`
`vec(tau) = hat(i) (20 - 6) - hat(j) (35 + 8) + hat(k) (-21 - 16)`
`vec(tau) = 14 hat(i) - 43 hat(j) - 37 hat(k) Nm`
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Find the work done in moving a particle along a vectors vec(S)=(hat(i)-2hat(j)+3hat(k))m if applied force is vec(F)=(2hat(i)-3hat(j)+4hat(k))N .

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Knowledge Check

  • The point of inersection of the line vec(r)=(hat(i)-hat(k))+t(3hat(i)+2hat(j)+7hat(k))" and the plane "vec(r)=(hat(i)+hat(j)-hat(k))=8 is

    A
    `(8,6,22)`
    B
    `(3t+1,2t,7t-1)` for some value of t
    C
    `(-8,-6,-22)`
    D
    `(x-1)/(3)=(y-0)/(2)=(z+1)/(7)=" for some value of t "`

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