define ratio theoram
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This theorem is very useful for finding the coordinates of a point that divides a line into a certain ratio. If P is any point on a line AB, and if, a, b and p are the position vectors of A, B and P respectively, then. p = λa + μb.
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Scalar Product and the Ratio Theorem
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HomeYear 11 (Yr 12 NZ, KS 4)Year 11 TopicsScalar Product and the Ratio Theorem
Scalar Product
Vectors can be added and subtracted and also multiplied by a constant. Vectors can also be multiplied.
The scalar product, or dot product, of two vectors a and b, in two or three dimensions, is defined as the product of their lengths and the cosine of the angle between their directions. It is written a.b and in words is said as "a dot b".
a.b = |a||b| cos θ
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