What is the magnitude of the vector (1, 1)?

The magnitude of the vector (1, 1) is √2.

To find the magnitude of a vector, we use the Pythagorean theorem. A vector in two dimensions, like (1, 1), can be thought of as a right-angled triangle where the components of the vector are the lengths of the two perpendicular sides. In this case, both sides are 1 unit long.

The formula for the magnitude of a vector (a, b) is √(a² + b²). For the vector (1, 1), we substitute a = 1 and b = 1 into the formula. This gives us √(1² + 1²), which simplifies to √(1 + 1) or √2. Therefore, the magnitude of the vector (1, 1) is √2.

Understanding the magnitude of a vector is important because it tells us the length or size of the vector, regardless of its direction. This concept is widely used in physics, engineering, and computer graphics, among other fields. For GCSE Maths, being able to calculate the magnitude of a vector is a fundamental skill that helps in solving more complex problems involving vectors.