How do you express vector g in terms of direction and magnitude?

Vector g can be expressed in terms of its magnitude and the direction it points in.

To express a vector in terms of its magnitude and direction, you first need to understand what these terms mean. The magnitude of a vector is its length, which can be found using Pythagoras' theorem if you know its components. For example, if vector g has components (gx, gy), its magnitude |g| is calculated as √(gx² + gy²).

The direction of a vector is the angle it makes with a reference axis, usually the positive x-axis. This angle can be found using trigonometry. For vector g with components (gx, gy), the direction θ can be found using the tangent function: θ = arctan(gy/gx). This gives you the angle in degrees or radians.

So, if you have a vector g with components (3, 4), its magnitude |g| would be √(3² + 4²) = 5. The direction θ would be arctan(4/3), which is approximately 53.13 degrees. Therefore, vector g can be described as having a magnitude of 5 units and pointing in a direction of 53.13 degrees from the positive x-axis.

Understanding vectors in terms of magnitude and direction is crucial in many areas of maths and physics, as it helps to visualise and analyse forces, velocities, and other vector quantities.