… d = displacement vector
… then what will be the diagram if we use the cosine rule … this is my question.
I still do not understand
why you posted four diagrams with coordinate axes.
Two of the diagrams show a line segment connecting points A and B. They labeled this line: vector
d. But, they don't show its direction! Which end of vector
d is the head? (Very sloppy.)
Additionally, they seem to be talking about
position vectors. If they want to represent vector
d as a position vector, then they have not correctly positioned it.
Regarding
your question above, diagrams do not change if somebody chooses to use the Law of Cosines. Also, the Law of Cosines doesn't care whether you have a diagram, whether you're working with vectors or simply a triangle, or what you're thinking or doing otherwise. The Law of Cosines is just a way to find the
length of the third side of a triangle.
This situation (contrasting diagrams with theorems) is the same concerning other theorems, like the Pythagorean Theorem, for example. A theorem doesn't care whether you have a drawing, what the drawing
represents or why you drew it. AND, if you choose Pythagorean Theorem to find hypotenuse length (versus some other method), the diagram does not change!
I agree with Halls. We use the Law of Cosines to find the distance between points A and B. That length is
not a vector. It is the
magnitude of a vector.
I hope you find time to take a beginning class on vectors. You need both comprehension and experience, from a structured approach to learning. :cool: