Let x² + y² = 1; u² + v² = 1 and xu + yv = 0, then
Which of the above is/are true ?
- 1. x² + u² = 1
- 2. y² + v² = 1
- 3. xy + uv = 0
3 only
1 and 2 only
1, 2 and 3
2 and 3 only
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2019
Case 1: $u = -y, v = x$.
Statement 1: $x^2 + u^2 = x^2 + (-y)^2 = x^2 + y^2 = 1$. (True, since $x^2+y^2=1$)
Statement 2: $y^2 + v^2 = y^2 + x^2 = x^2 + y^2 = 1$. (True, since $x^2+y^2=1$)
Statement 3: $xy + uv = xy + (-y)(x) = xy – xy = 0$. (True)
Case 2: $u = y, v = -x$.
Statement 1: $x^2 + u^2 = x^2 + y^2 = 1$. (True, since $x^2+y^2=1$)
Statement 2: $y^2 + v^2 = y^2 + (-x)^2 = y^2 + x^2 = 1$. (True, since $x^2+y^2=1$)
Statement 3: $xy + uv = xy + (y)(-x) = xy – xy = 0$. (True)
In both possible scenarios derived from the given conditions, all three statements hold true.