Vectors

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

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.

Properties

• Area of a parallelogram

Scalar Triple Product

Properties

• Swapping any 2 vectors will negate the product.
• iff , , are coplanar.
• Volume of a parallelepiped with , , as adjacent edges =
• Volume of a tetrahedron with , , as adjacent edges =

Vector Triple Product

Resulting vector lies in the plane that contains and .