Embedded Files
Key Ideas
Key Ideas
Explain how the in-product of two vectors relates to the cosine rule.
Understand that 3D systems of axes are not always the same in other cultures (movie: "Independence Day")
and much more
AHL 3.13 Angle between vectors
AHL 3.13 Angle between vectors
We learn how to calculate the angle between two vectors. The formula is given and 2 examples are worked through, with both 2D and 3D vectors. Working is clearly shown.
AHL 3.14 Kinematics
AHL 3.14 Kinematics
Kinematics: Position, speed and velocity of objects
https://www.youtube.com/watch?v=pFJmxD2mQ6w
We learn how to derive the formula for the cross product, or vector product, of two vectors using the determinant of a 3 by 3 matrix.The method is clearly explained and assume no prior knowledge of matrices.
AHL 3.16 The Cross Product (Vector Product)
AHL 3.16 The Cross Product (Vector Product)
We learn how to calculate the cross product using the determinant of a 3 by 3 matrix, by working through a detailed example. The cross product is also known as the vector product. The method we learn here will allow us to find calculate it without having to memorize the formula.
https://www.youtube.com/watch?v=f036SIfypZo
AHL3.17 Cartesian Equation of a plane
AHL3.17 Cartesian Equation of a plane
We learn how to find the cartesian equation of a plane, given three points that are contained in it. In the worked example we follow 3 steps: - find 2 non parallel vectors contained in the plane (do this use the 3 points given) - find a normal to the plane (by finding the vector product of the two vectors found above) - use the scalar product form of a plane's equation to find the cartesian equation the method is clearly explained through a detailed worked example.
AHL 3.18 Distance from a point to a plane
AHL 3.18 Distance from a point to a plane
We find the distance of a point P from a plane by finding the distance from P to its perpendicular projection Q on the plane. We find the vector equation of the line passing through P and Q, we then find the point of intersection of the line with the plane, that's the point Q. Finally we calculate the magnitude of the vector PQ. The three step method is explained in detail by working through an example.
AHL 3.18 Point of intersection of a line and plane
AHL 3.18 Point of intersection of a line and plane
We learn how to find the point of intersection of a line and a plane. We start by writing the line equation in parametric form. We then substitute the parametric expressions for x, y and z into the plane's equation and solve for the parameter lambda. Once we have lambda we calculate the coordinates of the point of intersection using the line's vector equation. The method is clearly explained step by step by working through a clear example.
AHL 3.18 Where a line meets a plane
AHL 3.18 Where a line meets a plane
https://youtu.be/kh25jr-KX6I
AHL 3.18 Angle between planes
AHL 3.18 Angle between planes
We learn how to find the angle between 2 planes with a worked example. We use the fact that the angle between two planes is equal to the angle between their normals. Using the planes' cartesian equations, that are given, we define the normals and then use the dot product formula for the angle between two planes to find the angle. The method is clearly explained as we work through the example.
AHL 3.18 Angle between a line and a plane
AHL 3.18 Angle between a line and a plane
Learn how to find the angle between a line and a plane in 3d space. We explain and derive the formula using the sine of the angle between the normal to the plane and the line's direction vector. We then use the formula to work through an example.
More AHL3.18 Intersections of planes
More AHL3.18 Intersections of planes
Finding intersections of planes using Rref on your calculator
(Reduced Row Echelon Form)
https://www.youtube.com/watch?v=a63b9hs_v-Q
AHL 3.18 The foot of the perpendicular
AHL 3.18 The foot of the perpendicular
Finding the foot of a perpendicular given vector componentsÂ
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