SS2 Second Term Further Mathematics Lesson Note – Vectors in Three Dimensions

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WEEK FOUR

VECTORS IN THREE DIMENSIONS

CONTENTS

(a) Scalars Product of Vectors in Three Dimensions

(b) Application of Scalar Product

SUB TOPIC: SCALAR PRODUCT OF VECTORS IN THREE DIMENSIONS

The scalar product of three vectors a,b and c is defined as a.(bxc) which is a scalar quantity.

If three vectors a,b and c are given as:

a = a₁i + a₂j + a₃k

b = b₁i + b₂j + b₃k

c = c₁i + c₂j + c₃k

The scalar product is found the same way as the determinant of a 3×3 matrix.

 

We denote dot or scalar product of two vectors A and B by A.B. This dot product is defined as the product of the magnitudes of A and B and the cosine of the angle between them.

A.B =

Scalar product otherwise called dot product (or inner products).

The Scalar product between two perpendicular vectors is zero.

Summary of the scalar product of unit vectors is provided below:

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