What is a scalar and what is a vector?
A quantity which does not depend on direction is called a scalar quantity. Vector quantities have two characteristics, a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction.
Why the current is scalar quantity?
Electric current is a scalar quantity. In the case of electric current, when two currents meet at a junction, the resultant current of these will be an algebraic sum and not the vector sum. Therefore, an electric current is a scalar quantity although it possesses magnitude and direction.
Is stress a scalar or vector?
The restoring force developed per unit area of a deformed body is called stress. It is a vector physical quantity.
What is the formula of AB vector?
dot product
| A · B = | (Ax î + Ay ĵ + Az k̂) · (Bx î + By ĵ + Bz k̂) | |
|---|---|---|
| A · B = | Ax î | · |
| + | Ay ĵ | · |
| + | Az k̂ | · |
| A · B = | AxBx + AyBy + AzBz | |
What is the formula for resultant vector?
Suppose two ships are moving in different directions at some angle between them and we have to find the distance between them we use the formulaR2=a2+b2−2abcosθ But if we have to find the resultant between two forces we use the formulaR2=a2+b2+2abcosθ.
How is AxB calculated?
Magnitude: |AxB| = A B sinθ. Just like the dot product, θ is the angle between the vectors A and B when they are drawn tail-to-tail. Direction: The vector AxB is perpendicular to the plane formed by A and B. Use the right-hand-rule (RHR) to find out whether it is pointing into or out of the plane.
Is AB the same as AxB?
1, pages 145-147). It’s an intuitive notation. 3b seems to imply you have three b’s. ab seems to imply you have a b’s.
What is the value of I cross I?
The value of i cap × i cap is equal to 0. Hence, the value of i cap × i cap is equal to 0.
What is the point of a unit vector?
The only purpose of a unit vector is to specify the direction of the force vector along a line with respect to the origin, hence why it’s magnitude is only one. The total force in three dimensions is the magnitude of its components, and the individual forces are the coordinate forces divided by its magnitude.
What is a unit vector and how is it important?
Unit vectors are vectors whose magnitude is exactly 1 unit. They are very useful for different reasons. Specifically, the unit vectors [0,1] and [1,0] can form together any other vector.