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What is power the quotient of physical science?

Power is the quotient of work and time. It is also defined as the rate at which any work is done. Work done is equal to the product of force and the displacement. The mathematical formula of power is given by : The SI unit in which power is measured is watts.

Why is work a scalar?

Work is a scalar quantity because it is the dot product of two vectors (Force and displacement). So, work done has only magnitude but not direction. Work done may be positive, negative or zero. This does not mean that it has a direction.

How do you work out the dot product?

About Dot Products bn> we can find the dot product by multiplying the corresponding values in each vector and adding them together, or (a1 * b1) + (a2 * b2) + (a3 * b3) …. + (an * bn). We can calculate the dot product for any number of vectors, however all vectors must contain an equal number of terms.

What is the dot product equal to?

Geometrically, the dot product of A and B equals the length of A times the length of B times the cosine of the angle between them: A · B = |A||B| cos(θ).

What does a dot product represent?

The dot product tells you what amount of one vector goes in the direction of another. So the dot product in this case would give you the amount of force going in the direction of the displacement, or in the direction that the box moved.

Is dot product always positive?

Answer: The dot product can be any real value, including negative and zero. The dot product is 0 only if the vectors are orthogonal (form a right angle). If the dot product is 0, the cosine similarity will also be 0.

What will happen if all components of a vector are reversed in direction?

Originally Answered: What will happen if all the components of a vector are reversed in direction? Thus, reversing the direction of all components of a vector simply gives you the negative of the original vector (which, of course, is the same thing as reversing the vector).

What if two vectors are collinear?

Condition of vectors collinearity 2. Two vectors are collinear if relations of their coordinates are equal. Two vectors are collinear if their cross product is equal to the zero vector.

What is the condition for two vectors to be parallel?

Two vectors are parallel if they are scalar multiples of one another. If u and v are two non-zero vectors and u = cv, then u and v are parallel.

How do you know if two parametric lines are parallel?

we can choose two points on each line (depending on how the lines and equations are presented), then for each pair of points, subtract the coordinates to get the displacement vector. If the two displacement or direction vectors are multiples of each other, the lines were parallel.

When can the sum of two vectors be minimum and maximum?

The sum of two vectros is maximum , when both thectros are in the same direction and is minimum when they act in opposite directions.

What is the angle between two vectors when their sum is minimum?

180 degree

When can the addition of two vectors be zero?

Addition of two vectors can only be zero when there directions are opposite and their magnitude is additive inverse of each other.

Can the sum of two vectors be a scalar?

No, it is impossible for the magnitude of the sum to be equal to the sum of the magnitudes.

What is the sum of two vectors called?

The sum of two or more vectors is called the resultant.

Why can’t you add a scalar to a vector?

While adding a scalar to a vector is impossible because of their different dimensions in space, it is possible to multiply a vector by a scalar. A scalar, however, cannot be multiplied by a vector.

Can the sum of two vectors be equal to either vector?

If you mean that the sum of 2 vectors is equal to either vectors in terms of magnitude and direction, then no, unless both vectors are zero vectors. However, the direction of the sum of 2 vectors can be same as direction of either vectors provided that both vectors are parallel.

Will the sum of 2 vectors always be bigger than the magnitude of one of the vectors?

The magnitude of the sum of two vectors is always less than the sum of the magnitudes of the two vectors. A vector’s component can never be larger than the magnitude of the vector. It is possible for a vector to be zero, while a component of the vector is not zero.