)A vector calculation is a mathematical operation that involves manipulating vectors, which are quantities that have both magnitude and direction.
The formula for finding the magnitude of a vector is √(x^2 + y^2 + z^2), where x, y, and z are the components of the vector in three-dimensional space.
To find the magnitude of a vector using the Pythagorean theorem, you square each component of the vector, sum the squares, and then take the square root of the sum. For example, if a vector has components (3,4,5), the magnitude would be √(3^2 + 4^2 + 5^2) = √(9 + 16 + 25) = √50 = 7.07.
Vectors have both magnitude and direction, while scalars only have magnitude. For example, velocity is a vector quantity because it has both magnitude (speed) and direction, while speed is a scalar quantity because it only has magnitude.
To find the difference of two vectors, you subtract the components of the second vector from the components of the first vector. For example, if v = (2,3) and w = (1,4), then v-w = (2-1, 3-4) = (1,-1). This can also be represented as v-w = (1,-1) or ⎮v-w⎮ = √(1^2 + (-1)^2) = √2.