Vectors in Two Dimensions

You will be able to

• Find the vector AB = b − a from position vectors, and give it in i, j form, as a column vector and with its exact magnitude.
• Calculate the unit vector in the direction of a vector, and a vector of given magnitude in that direction.
• Solve λa + μb = c for the scalars λ and μ by equating the i and j components and solving the simultaneous equations.

You will be able to

• Calculate a resultant velocity as a vector sum, giving its speed and its direction as an angle to the bank or a three-figure bearing.
• Determine the time to cross a river from the component of velocity across it, and the distance carried downstream.
• Use r = r₀ + tv to find the position of a moving object at time t, and the time at which it reaches a given point.