Why does the magnetic flux have size and direction, and it is scalar, and is the area positive or negative?

Why does the magnetic flux have size and direction, and it is scalar, and is the area positive or negative?

The magnetic flux D Φ of a surface element DS passing through a magnetic field is defined as the product of the magnetic induction B and the projection dscos θ of DS in the direction perpendicular to B, that is, D Φ = bdscos θ, where θ is the angle between the normal direction n of the surface element and the magnetic induction B. the magnetic flux is a scalar, θ < 90 ° is a positive value, and θ > 90 ° is a negative value, But it can be divided into positive and negative. Generally speaking, the plane through which the magnetic induction line passes has two sides. Let a and B be the reference plane. If the magnetic induction line passes through the plane from B, it will be negative; otherwise, it will be positive. Generally speaking, the area has no positive or negative. If we see positive or negative, it includes the angle product in the formula. From the formula, we can see that the positive or negative of the magnetic flux depends on the angle between the magnetic induction intensity and the normal direction of the plane

The question of whether velocity and work are vectors or scalars
Don't be ignorant when you are a beginner
Just like the definition of vector: there are physical quantities with both size and direction. Then the definition of speed is: the physical quantity that represents the speed of an object's motion. According to my understanding, speed has no direction, so why is speed a vector?
Scalar is defined as having only size and no direction. When an object is acted by a force and moves a certain distance in the direction of the force, we say that the force does work on the object. "In the direction of the force" is there a direction? Why is work scalar?

The definition of speed in middle school books is not accurate. The more accurate definition of speed should be "the physical quantity representing the motion state of an object", which includes both size and direction
As for work, work is a process quantity, which describes the accumulation effect of force in the process of displacement of an object along the direction of force. It can also be said that it is the spatial accumulation effect of force. From this point of view, it is really impossible to explain this problem. However, there is another better definition of work: work is the measure of mechanical energy in the transformation process, that is "the change of mechanical energy", Since mechanical energy is scalar, work is also scalar
In addition, don't be misled. Although every middle school (or even University) textbook says that vector is a physical quantity with both size and direction, scalar has only size but no direction. In fact, it's far from easy to distinguish vector and scalar, and physical quantity is not only scalar and vector. For example, the "work" mentioned above is a good example, In addition, there is a better example, the current intensity has a size and direction, but it is a scalar. To strictly distinguish scalar from vector, we need to use the relevant knowledge of matrix, tensor algebra, and the combination of degrees of freedom and other professional terms
In senior high school, we only need to remember which are scalar, which are vectors, and the addition and subtraction, number multiplication and point multiplication between vectors. We will understand it in the future

Does voltage and current have scalar and vector in Electrotechnics?

Scalar but with positive and negative (direction)
Unlike vector, vector can be added by vector (parallelogram rule), but scalar cannot