Solving Vector Problems

Solving Vector Problems-43
Many students are often reluctant to tackle questions using vectors.I think this is partly because often vectors is not taught until quite a way through a school maths course, so they are unfamiliar.

Many students are often reluctant to tackle questions using vectors.I think this is partly because often vectors is not taught until quite a way through a school maths course, so they are unfamiliar.Consider the point on the tire that was originally touching the ground.

Scalar products Scalar products are immensely useful!

Sometimes if you're at a loss to know what to do with vectors and vector equations, it's worth just taking the scalar product of the whole equation with one of your vectors and seeing what you end up with.

We are very used to expressing lines using cartesian geometry in the form $y=mx c$ and other variants.

The vector equation of a line is no more complicated really, it's just a case of getting used to it.

Start by solving vector problems in two dimensions - it's easier to draw the diagrams - and then move on to three dimensions.

(For four or more dimensions, it becomes more difficult to visualise!Sometimes it's useful to draw on lines parallel and perpendicular to my coordinate axes so I can make sense of the x and y components of a vector.Given a vector problem, a quick sketch can help you to see what's going on, and the act of transferring the problem from the written word to a diagram can often give you some insight that will help you to find a solution.Then we may be informed that a vector is "simply" a quantity that has both magnitude and direction (unlike a scalar which only has magnitude).Diagrams It is helpful to separate out some of these ideas about vectors in order to make sense of things.For example, you and a friend might both be pulling on strings attached to a single block of wood.Find the magnitude and direction of the resultant force in the following circumstances.a) The first force has a magnitude of 10 N and acts east.The Greek letters $\lambda$ and $\mu$ are often used as constants in vector equations, so why not get into the habit of using them for yourself? (moderate) A car moves 150.0 m at a 63° "north of east" (this simply means 63° from the x-axis).Working out how the magnitude and direction change over time can help you to picture the situation.Vector equation of a line Some students are intimidated by the vector equation of a line when they first meet it.

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