yr2 chap 12 vectors

• coordinates in 3D are written in the form (x, y, z)
• you can write 3D vectors as column vectors in the same way you would with 2D vectors by adding a third number below the others in the bracket to represent the z axis
• to find the distance between a point and the origin, use 3D pythagoras, in the form: distance^2 = x^2 + y^2 + z^2
• the magnitude of a vector is the distance between the origin and the point so can be found using 3D pythagoras
• to find the distance between two points (x, y, z) and (a, b, c) in 3D, use 3D pythagoras in the form: distance^2 = (a-x)^2 + (b-y)^2 + (c-z)^2
• use column notation where possible because it is easier to do calculations with
• a unit vector is any vector with a magnitude of 1
• to find a unit vector, divide the vector by the magnitude of the vector
• to find the angle between a vector (xi, yj, zk) and any of the 3 axes, use the formulae:

  cos theta(x) = x / |v|

  cos theta(y) = y / |v|

  cos theta(z) = z / |v|