If a and b makes an angle ⁻¹ ( 5 9 ) with each other, then | a + b |= 2 | a - b | for | a |=n| b | The integer value of n is ____

Step-by-step solution

aligned & = 5 9 & a b a b = 5 9 & a^2+b^2+2 a b =2 a^2+2 b^2-4 a b & 6 a b =a^2+b^2 aligned aligned & 6 5 9 a b=a^2+b^2 & 10 3 a b=a^2+b^2 & a=n b & 10 3 n b^2=n^2 b^2+b^2 & 3 n^2-10 n+3=0 & n= 1 3 and n=3 aligned integer value n=3