What is the magnitude of vector (24, 7)?

The magnitude of the vector (24, 7) is 25.

To find the magnitude of a vector, we use the Pythagorean theorem. The vector (24, 7) can be thought of as a right-angled triangle where 24 and 7 are the lengths of the two perpendicular sides. The magnitude of the vector is the length of the hypotenuse of this triangle.

The formula to calculate the magnitude of a vector (a, b) is √(a² + b²). In this case, a is 24 and b is 7. So, we substitute these values into the formula:

Magnitude = √(24² + 7²)
= √(576 + 49)
= √625
= 25

Therefore, the magnitude of the vector (24, 7) is 25. This means that if you were to draw this vector on a graph, the straight-line distance from the origin (0, 0) to the point (24, 7) would be 25 units. Understanding how to calculate the magnitude of a vector is a fundamental skill in GCSE Maths, especially when dealing with problems in geometry and physics.