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What are the applications of cross product and dot product in physics?
cross: torque dot: work
How power is dot product of force and velocity?
The dot product of force and velocity gives the power generated by the force on the object. It is calculated as the product of the magnitudes of force and velocity, multiplied by the cosine of the angle between them. This represents the rate at which work is done on the object by the force.
How much work is done when a vertical force acts on an object moving horizontally?
as work done is dot product of force and displacement so cos(90)=0;therfore work done is zero
Is work is the vector product of force and distance?
Yes and no. It's the dot product, but not the cross product.
How the power is the dot product of force and velocity?
The power is given by the dot product of force and velocity because it captures the component of force that is acting in the direction of velocity. This means that only the force that is contributing to the motion of the object is considered in calculating the power transferred to the object. The dot product helps isolate this specific component and quantify the rate at which work is being done.
Where is the resultant vector lies when dot product of two vector is done?
arithmetic mean
What is dot products and give some examples?
A Dot product is a very useful tool in both mechanics and 3D graphics. It calculates the cosine of the angle between two vectors.In two-dimensional space, the dot product of vectors [a, b] and [c, d] is ac + bd.Mechanical work is the dot product of force and displacement vectors.Magnetic flux is the dot product of the magnetic field and the area vectors.
What is vector dot product?
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
How is dot product of vectors used?
The dot product of vectors is used to determine the angle between them and to calculate projections. It quantifies how much one vector extends in the direction of another, which is useful in physics for work calculations (force along a displacement) and in computer graphics for lighting and shading effects. Additionally, the dot product can indicate orthogonality; if the dot product is zero, the vectors are perpendicular.
What is the work done by a body moving along a circular path?
The work done by a body moving along a circular path is zero if the force is perpendicular to the direction of motion, such as in the case of centripetal force. This is because the displacement is perpendicular to the force. If there is a component of the force in the direction of the motion, work is done, calculated as the dot product of the force and displacement vectors.
What can be said about a situation in which work done is negative?
the formula F.S cos angle is used (the dot product) so if angle is 0,cos angle=1 hence work done is positive and maximum if angle is 90 so cos 90 is 0 hence work done is minimum if work done is negative the angle is 180 The work done by friction is always negative (opposite the force) Since work is force x displacement, a negative value for work could mean that the displacent was negative
What is the gradient of a dot product and how is it calculated?
The gradient of a dot product is a vector that represents the rate of change of the dot product with respect to each variable. It is calculated by taking the derivative of the dot product with respect to each variable and combining them into a vector.
