a. Please provide a well explained answer for the follwoing. And explain what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a scalar k, what is kv (geometrically and algebraically)? -v?
a. Please provide a well explained answer for the follwoing. And explain what are the components of a
Components of vector
In two dimensional ,any vector can divide into two components x - component(horizontal component)
and y - component(vertical component).
As we can see in the figure , then it has two components ( components are not vectors)
where vx is x- component (horizontal ) and is y- component (vertical)
Also vx = vcos
= vsin
where is angle between vector and x-axis (positive direction).
(ii) What if the initial point is not (0,0)
If the vector has not initial point is origin , then it is a shifted vector
Let initial point is (h ,k) and we have vector v(x ,y)
then our new vector (x' , y') which started from origin is (x- h, y-k)
In the figure , we have two co-ordinate systems , in the old system vector is (x, y) with starting point (h ,k)
But , in the new co-ordinate system(shifted the origin from (0,0) to (h, k) ), our vector is (x-h, y-k)
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