A spacecraft located at î + 2ĵ + 3k̂ is subjected to a force λ k̂ by firing a rocket. The spacecraft is subjected to a moment of magnitude

Concept:

1. Moment: It will be equal to the cross product of a position vector r from the point to anywhere on the line of action of the force and the force vector itself.⇔ 
2. Cross product of two vectors: The cross product can be written as a determinant.
   Let  and  be the two vectors. ⇒ and 
   
3. If   then determinant of A is given by:
   |A| = a₁₁ × {(a₂₂ × a₃₃) – (a₂₃ × a₃₂)} - a₁₂ × {(a₂₁ × a₃₃) – (a₂₃ × a₃₁)} + a₁₃ × {(a₂₁ × a₃₂) – (a₂₂ × a₃₁)}
    
4. Magnitude of vector: Let  
   Magnitude of vector of a = 

Calculation:

Given: 

We have to find magnitude of moment,

We know that, 

Now,

Magnitude of moment =  = √5 λ