i have a doubt here..
the question is:
if [a vector+3(b vector)] is perpendicular to [7(a vector)-5(b vector)] and [a vector-5(b vector)] is perpendicular to [7(a vector)+3(b vector)].find the angle between a vector and b vector.
This problem is a simple one and on solving one can readily obtain the solution as the angle to be 90 degrees.
But considering the first and second equations of the two perpendicular vector cases,you may find that arbitary values of a and b do not necessarily satisfy the equations.In that cases there is a contradiction of the vectors not being perpendicular.How is that possible?
I hope you have understood my question.If not,please solve the question by expanding using scalar product and you will know where the fault lies.
The apparent fallacy seems to lie in choosing arbitrary values of variables that are related in defined ways. Perhaps a crude analogy would be this:
Consider the following equations:
2x + 3y = 5
x - 3y = 4
The solution for this is x=3, y=-1/3.
Here, any arbitrary values of x and y cannot be substituted in the given equations.
In fact this is the difference between the identity and equation.
Consider the following equations:
2x + 3y = 5
x - 3y = 4
The solution for this is x=3, y=-1/3.
Here, any arbitrary values of x and y cannot be substituted in the given equations.
In fact this is the difference between the identity and equation.