Last time I have written about the properties of unit vectors that is:

Dot product of unit vectors :

i.i=1

j.j=1

k.k=1

i.j=j.k=k.i=0

Do you know how the above results come? If your answer is no, then let us discuss it:

I have already explained in my earlier articles that dot product or scalar product between two vectors A and B is given as:

A.B = AB cos θ

where θ is the angle between A and B. A and B are magnitudes of A and B.

As i the unit vector along x axis

Therefore i.i = 1cos 0

This is because, first i is the unit vector of A along x axis and second i is the unit vector of B along x axis.

Therefore two unit vectors must be in the same direction that is x direction so the angle between them will be 0 degree. As i and i are unit vectors therefore there magnitudes will be unity.

Therefore above equation will become: i.i =1

Similarly

j.j =1

k.k =1

Then why i.j =0,

This is because, I along x axis and y along y axis, thus, angle between them will be 90 degree.

Therefore, i.j = 1 cos 90

i.j = 0

Similarly

j.k=k.i=0

Note: I hope that now you can understand and explain everything about the dot or scalar product of two unit vectors.

Reference: These articles are referred from my authored book “concepts of electromagnetic field theory” having ISBN 978-81-272-5245-8. Try to make the figures for products of vectors. In case of any doubt in this article or any other EMFT or physics related article, kindly post in the comment section.