the position vectors of A and B relative to the origin are a and b repsectively
The point P is on OA such that PA=2PA
So my question is if B is the top of the triangle and O represent the left corner of the triangle and A the right corner, where would place the point P on the triangle??
To determine the position of point P on the triangle, we can use vector addition and scalar multiplication.
Let's assume that vector OA is given as vector a, and vector OB is given as vector b.
We know that PA = 2PA, which means the length of vector PA is twice the length of vector PB.
To find vector PA, we can use scalar multiplication. Since PA is twice the length of PB, we can write the equation as:
PA = 2 * PB
We can rearrange this equation as:
PA - 2 * PB = 0
Now, let's use vector addition to get vector PA:
PA = OB - OA
Substituting the values, we have:
PA = b - a
To find vector PB, we can use scalar multiplication by dividing vector PA by 2:
PB = (1/2) * PA
Substituting the value of PA, we get:
PB = (1/2) * (b - a)
Now, we have vectors PA and PB. To find point P, we need to find the sum of vectors OA and PA:
P = O + PA
Substituting the values of O and PA, we have:
P = O + (b - a)
Thus, the position of point P on the triangle is given by the vector sum of O and PA, which is equal to O + (b - a).