Question

to resolve a force f into a rectangular component, the force can be expressed as the:

• ratio between its magnitude and the unit vector λ.
• ratio between its magnitude and sine of the angle made with the x axis.
• product of its magnitude and sine of the angle made with the x axis.
• product of its magnitude and the unit vector λ.

Explanation:

To resolve a force \( F \) into rectangular components, the formula for a component (e.g., along a direction with unit vector \( \lambda \)) is the product of the force's magnitude and the unit vector \( \lambda \), or using trigonometry, if \( \theta \) is the angle with the \( x \)-axis, the \( x \)-component is \( F\cos\theta \) and \( y \)-component is \( F\sin\theta \). But the option "product of its magnitude and the unit vector \( \lambda \)" is correct as the component of a vector \( \vec{F} \) in the direction of unit vector \( \lambda \) is \( F \cdot \lambda \) (where \( F \) is the magnitude of \( \vec{F} \)). The other options: ratio is incorrect (it's a product), and the sine - related option is for a specific perpendicular component (not the general component along a unit vector direction).

Answer:

product of its magnitude and the unit vector \( \lambda \)