Quick Question-Vectors?

Question

When a rectangle is constructed in order to add velocities, what represents the resultant of the velocities? The diagonal right? Not a vertical side, the horizontal side or something else.

So the diagonal of the rectangle would be correct?

Answer 1

vectors...an old subject!
from my ageing brain, it should be diagonal right.
not able to explain diagrammatically here...
Let a=a1i + a2j + a3k and b=b1i + b2j + b3k.
The sum of a and b is:
The addition may be represented graphically by placing the start of the arrow b at the tip of the arrow a, and then drawing an arrow from the start of a to the tip of b.
:-)

Answer 2

We add vectors graphically by placing the tail of one (e.g., A) on the head of another (e.g., B) Conversely, we subtract vectors by putting them head to head.

The term "diagonal" only has meaning if the two vectors A and B are at right angles to each other, in which case they add up to a hypotenuse as in C^2 = A^2 + B^2 for a right triangle.

When you use a "rectangle" (two right triangles) to draw your vectors, you are ensuring the vectors A and B are at right angles to each other. If the tail of B is on the head of A, then the two vectors are added and the resulting value (C) can be obtained from C^2 = A^2 + B^2, where C is the hypotenuse or diagonal of the two right triangles making up the rectangle.

Answer 3

Suppose you need to add two vectors A -> B and C -> D (imagine that A, B, C and D are the points defining the vectors, and the symbol -> denoted the direction)

There are two ways to draw your diagram:

1) Draw your vectors in succession, meaning that the second one starts where the first one ends, i.e. B and C refer to the same point. In this case you can find their sum by connecting the beginning of the first vector (point A) with the end of the second vector (point D) i.e. vector A -> D.

2) Draw your vectors in such a way that they both start on the same point (i.e. A and C are the same point). From point B draw a line parallel to vector C -> D. Then from point D draw a line parallel to vector A -> B. Let's assume that these lines meet on point F.
In order to draw the sum vector, just join point A (or C, since, as we said, they are the same) and point F, so you get vector A -> F.

Needless to say that no matter what method you use you end up with the same result.

Also note that in the first method you may describe your sketch as a triangle, but in the second one it would be more appropriate to call it a parallelogram.

Answer 4

Hypotenuse

Answer 5

yup right ...the resultant of both vertical and horizontal ones