Home
Class 12
MATHS
A particle, in equilibrium, is subjected...

A particle, in equilibrium, is subjected to four forces `vecF_1, vecF_2, vecF_3` and `vecF_4`, ` vec F_1 =-10 hat k , vec F _2 =u(4/13 hat i-12/13 hat j+3/13 hatk) , vec F _3 =v(-4/13 hat i-12/13 hat j+3/13 hatk), vec F_4 =w(cos theta hat i+sin theta hat j) ` then find the values of u,v and w

Text Solution

Verified by Experts

Since, the particle is in equilibrium.
`F_(1)+F_(2)+F_(3)+F_(4)=0`
`-10hatk+u((4)/(13)hati-(12)/(13)hatj+(3)/(13)hatk)+v(-(4)/(13)hati-(12)/(13)hatj+(3)/(13)hatk)+w(costhetahati+sinthetahatj)=0`
`implies((4u)/(13)-(4v)/(13)+wcostheta)hati+((-12)/(13)u-(12)/(13)v+wsintheta)hatj+((3)/(13)u+(3)/(13)v-10)hatk=0`
`implies(4u)/(13)-(4v)/(13)+wcostheta=0` . . . (i)
`-(12)/(13)u-(12)/(13)v+wsintheta=0` . . . (ii)
`(3)/(13)u+(3)/(13)v-10=0`
From Eq. (iii), we get `u+v=(130)/(3)`
From eq. (ii), we get
`-(12)/(13)(u+v)+wsintheta=0`
`implies-(12)/(13)((130)/(3))+wsintheta=0`
`implies w=(40)/(sintheta)=40` cosec `theta`
On substituting the value of w in eqs. (i) and (ii), we get
`u-v=-130cot theta`
and `u+v=(130)/(3)`
On solving we get
`u+(65)/(3)-65 cot theta`
`v+(65)/(3)+65cot theta and w=40" cosec "theta`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

A particle,in equilibrium,is subjected to four forces vec F_(1),vec F_(2),vec F_(3) and vec F_(4)vec F_(1)=-10hat k,vec F_(2)=u((4)/(13)hat i-(12)/(13)hat j+(3)/(13)hat k),vec F_(3)=v(-(4)/(13)hat i-(12)/(13)hat j+(3)/(13)hat k),vec F_(4)=w(cos thetahat i+sin thetahat j) then find the values of u,v and w

If vec a=2hat i+2hat j-3hat k,vec b=hat i-2hat j+2hat k,vec c=4hat i+3hat j+3hat k then find the value of |vec a+2vec b+2vec c|

If vec A = hat i + 3 hat j + 2 hat K and vec B = 3 hat i + hat j + 2 hat k , then find the vector product vec A xx vec B .

If vec a=3hat i+4hat j and vec b=hat i+hat j+hat k, find the value of |vec a xxvec b|

vec a=4hat i-hat j+hat k+hat k,vec b=2hat i+hat j+7hat k,vec c=-3hat i-4hat j+2hat k and vec d=hat i+hat j+hat k then find the value of 3vec a+2vec b-4vec c-vec d

If vec a=3hat i-2hat j+4hat k and vec b=hat i-hat j+2hat k then find the modulus of vec a-vec b

Prove that the vectors vec A = 4 hat i + 3 hat j + hat k and vec B = 12 hat i + 9 hat j + 3 hat k are parallel to each other.

If vec A =4 hat I + 6 hat j -3 hat k and vec B =- 2 hat I -5 hat j + 7 hat k , find the angle between vec A and vec B .

If vec A=hat I + 2 hat j -3 hat k , vec B =2 hat I -hat j + hat k and vec Chat I -3 hat j + 2 hat k , then find vec A xx ( vec B xx vec C).

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot