Dot product (or scalar product, since it is found by multiplying 2 magnitudes
and
)
) , as you know is given by:
its called dot product cause we use a dot to show the multiplication btw!
In essence, I think what you work out, most of the time is the angle between two vectors.
This comes into play when considering if vectors are parallel or perpendicular to each other, and thus this can help in proving something like a quadrilateral, square, rhombus, trapezium...
also in a physical aspect, it can be used in cases such as:
REFER TO ATTACHMENT HERE
im gonna show some applied physics here so skip on if you wish!
the stickfigure is pulling the object with a constant force (vector quantity)
so that it moves along the horizontal ground right.
Consider the following:work done = our dot product in this example
the work done in physics, is work done = force x displacement - 2 vector quantities
the
component of the force being applied, as in the right diagram, in the direction of motion =
so the work done, through a distance of
is thus given by the distance moved(i.e
), ,
multiplied by the
magnitude of the component of the force, in the direction of motion, i.e.
this then gives us our:
, where
is the angle between a and b when they are placed
TAIL TO TAIL ! in a physics sense, to use the least possible force, we would need to pull horizontally, so that we are pulling in the same direction as we want the object to move. Then we would have θ = 0 and cos θ= 1 so that the work done
, which = magnitude of the force multiplied by the distance moved in the direction of the force.
So...! don't dwell too much cause i dont think we need to go that far, however keep in mind the usefulness of the dotproduct and the applications of it, since who knows.. a question , maybe similarly described above might happen to appear on the exam. AND I HOPE IT DOES SO I GET 10/10.
haha nah. yer hope that helped...
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