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Introduction to Vectors

Revise Vectors unit from G.C.E (A/L) Combined Mathematics.

Section formula

Suppose is the reference point, and are 2 points.

If divides the line segment in the ratio (both are positive and ), the division can either be internal or external.

Internally

Externally

Direction Cosines

Suppose . Direction cosines of are where are the angles makes with axes.

Unit vector in the direction of . Because of this:

Direction Ratio

Ratio of the direction cosines is called as direction ratio.

Cross Product

is the unit normal vector to and . Direction is based on the right hand rule.

Cross products between , , are circular.

Cross products of i,j,k

Properties

Scalar Triple Product

iff , , are coplanar. Swapping any 2 vectors will negate the product.

Vector Triple Product

Resulting vector lies in the plane that contains and