For the resultant of several vectors, its x-component

Step-by-step solution

Let the vectors be A ₁, A ₂, , A _n . The resultant vector is R = A ₁ + A ₂ + + A _n . Taking the x-component on both sides, R_x = A_ 1x + A_ 2x + + A_ nx . Thus, the x-component of the resultant equals the sum of the x-components of the individual vectors. The magnitude of the resultant satisfies | R | | A ₁| + | A ₂| + + | A _n| . Since the x-component of any vector cannot exceed its magnitude, R_x | R | . Combining these inequalities gives R_x | A ₁| + | A ₂| + + | A _n| . If all vectors are directed along the p