A vector is a mathematical quantity that has both magnitude and direction. It is usually represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction. Vectors are commonly used in physics and engineering to represent forces, velocities, and other physical quantities.
To add two vectors, you must first make sure they are in the same coordinate system. Then, you can add the corresponding components of each vector to get the resulting vector. For example, if vector A has components (3, 4) and vector B has components (1, 2), the resulting vector C would have components (3+1, 4+2), or (4, 6).
A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. For example, the distance traveled by a car is a scalar quantity, while the displacement of the car (which includes both distance and direction) is a vector quantity.
The magnitude of a vector is the length of the vector, and it can be found using the Pythagorean theorem. To find the magnitude, you square each component of the vector, add them together, and then take the square root of the sum. So, for a vector with components (3, 4), the magnitude would be √(3² + 4²) = √(9 + 16) = 5.
Yes, vectors can have negative components. This indicates the direction of the vector. For example, a vector with components (-3, 4) would have a magnitude of 5 and would be pointing in the direction of 180 degrees (or to the left on a coordinate plane).