Question

The torque of a force `5hat"i" + 3hat"j" - 7hat"k"` about the origin is τ. If the force acts on a particle whose position vector is `2"i" + 2hat"j" + hat"k"`, then the value of τ will be ______.

पर्याय

• `11hat"i" + 19hat"j" - 4hat"k"`

• `-11hat"i" + 9hat"j" - 16hat"k"`

• `-17hat"i" + 19hat"j" - 4hat"k"`

• `17hat"i" + 9hat"j" + 16hat"k"`

Answer 1

The torque of a force `5hat"i" + 3hat"j" - 7hat"k"` about the origin is τ. If the force acts on a particle whose position vector is `2"i" + 2hat"j" + hat"k"`, then the value of τ will be `underlinebb(-17hat"i" + 19hat"j" - 4hat"k")`.

Explanation:

Given that torque, `vecτ =5hat"i" + 3hat"j" - 7hat"k"`

position vector, `vec"r"=2hat"i" + 2hat"j" + hat"k"`

`vecτ=vec"r"xxvec"F" = |("i", "j", "k"), (2,2,1),(5, 3, -7)|`

= `hat"i"(-14-3)-hat"j"(-14-5)+hat"k"(6-10)`

= `-17hat"i" + 19hat"j" - 4hat"k"`