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- Maths and statistics
- Vectors and matrices
- Vectors
Imagine navigating a hilly landscape, searching for the steepest ascent or smoothest descent—this is the essence of directional derivatives. These mathematical tools are vital in meteorology for predicting temperature changes along wind paths, in finance for analysing portfolio shifts, and in machine learning for optimising algorithms. Use this resource to...
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- Maths and statistics
- Vectors and matrices
- Vectors
The distance between a point in 3D space and a plane can be determined using vectors and trigonometry. This is handy in many situations, like making sure components are specific distances from certain planes in construction, determining distances between a airplane and a mountain or building in safe flight planning,...
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Dynamics resources Worksheets Download the dynamics worksheets to improve your skills. Work, energy and power (PDF) Motion: Constant acceleration (PDF) Motion: Non-constant acceleration (worked solution) (PDF) Blocks & pulleys (worked solution) (PDF)...
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- Maths and statistics
- Vectors and matrices
- Vectors
Uniquely defining a line for a vector in three-dimensional space is useful in a range of scenarios. In mechanical and civil engineering, they are needed to create models and analyse alignment. In computer graphics, they can be used to define paths for animations. In physics, they represent trajectories of particles...
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- Maths and statistics
- Vectors and matrices
- Vectors
Just as we can define an equation for a line in three dimensions, we can do the same for an entire plane–that is, we can define an equation that represents a two-dimensional space within a 3D space. A plane is a subset of three dimensional space. You can think of...
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- Maths and statistics
- Vectors and matrices
- Vectors
Vectors can be used to determine whether two lines in 3D cross each other (or intersect), and identify the point at which they intersect. This is used in a variety of STEM disciplines, including detection of collisions between objects in robotics and modelling complex structures in computer graphics and game...
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- Maths and statistics
- Vectors and matrices
- Vectors
Two planes in 3D can intersect. Finding this intersection has many real-life applications, including the design of buildings in architecture, 3D rendering and modelling in computer graphics, and determining paths of movement in robotics. Use this resource to learn how to determine the angle between two intersecting planes and the...
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- Maths and statistics
- Vectors and matrices
- Vectors
Vectors are used to represent forces in physics, handle 2D and 3D manipulation with computer graphics, and to calculate the forces acting on materials in textiles. You also deal with vector quantities in your everyday life, from driving your car down the road to planning the shortest route to get...
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- Maths and statistics
- Vectors and matrices
- Vectors
You will have learned that vectors can be resolved in two dimensions along the horizontal and vertical axes. It is also possible to resolve one vector along the line of another vector, instead of along the \(x\)- and \(y\)-axes. Often, in physics, engineering and mathematics courses, you are asked to...
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- Maths and statistics
- Vectors and matrices
- Vectors
Breaking vectors down into their components—or resolving them—makes it easier to add or subtract them, especially when dealing with vectors that don't act along the same line. You will encounter this in many areas of STEM, like when analysing forces involved in robotics, studying the projectile motion of objects launched...
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- Maths and statistics
- Vectors and matrices
- Vectors
There are two ways to multiply two vectors. Here, we will learn about the scalar product. It has many applications in STEM. For example, scalar products are used to calculate the work done by a system, in computer graphics to calculate the amount of light hitting surfaces, and in engineering...
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- Maths and statistics
- Vectors and matrices
- Vectors
The vector product is another way to multiply two vectors. Just like scalar products, vector products have many broad applications, such as in electrical engineering, quantum physics, software development, game programming and statistics. Use this resource to learn more. The vector product is a vector resulting from multiplying the magnitudes...
