Dot Product of Two Vectors (Class 11 vector physics)

Dot product of two vectors: • Vector DOT PRODUCT (Cl...
If a force acts at an angle to displacement, the dot product of force and displacement gives the work done. Here dot product of the two vectors combines two vectors to yield a scalar quantity that is work. In the context of force and displacement, the dot product is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them.
F.d = work done by the force: The dot product of the force vector (F) and the displacement vector (d) represents the work done by the force.
Horizontal component of the force: When a force acts at an angle, it can be broken down into two components: one in the direction of the displacement (horizontal component) and another perpendicular to it (vertical component). The horizontal component of the force is given by FCosθ, where F is the magnitude of the force and θ is the angle between the force and displacement vectors.
Multiplication with displacement: The horizontal component of the force (FCosθ) is then multiplied by the displacement (d). This multiplication represents the work done by the horizontal component of the force in the direction of displacement.
Regrouping terms in the vector equation: When the terms in the equation involving vectors are rearranged or regrouped, the result is equal to the dot product of the force vector and the displacement vector. This implies that the work done by a force acting at an angle can be calculated using the dot product of the force and displacement vectors.
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