Question

Prove by vector method that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer 1

Given:- Right angle Triangle

To Prove:- Square of the hypotenuse is equal to the sum of the squares of the other two sides

Let ΔAOB be right angle triangle with right angle at O

Thus we have to prove

AB² = OA² + OB²

Proof: - Let, O at Origin, then

\(\vec a\) and  \(\vec b\) be position vector of A and B respectively

Since OB is perpendicular at OA, their dot product equals to zero

We know that,

Now, We can see that, by triangle law of vector addition,  \(\vec{AB}=\vec b-\vec a\) 

Therefore,

⇒ AB² = OA² + OB²(Pythagoras theorem)

Hence, proved.