JEE Main20202 Sep 2020Evening ShiftMathematicsMatricesActual
Let A = X = x , y , z T : P X = 0 and x 2 + y 2 + z 2 = 1 where P = 1 2 1 - 2 3 - 4 1 9 - 1 then the set A
Options
- AIs a singleton.
- BIs an empty set.
- CContains more than two elements
- DContains exactly two elements
Correct answer
D. Contains exactly two elements
Step-by-step solution
∵     P = 0 ∴ System of equations x + 2   y + z = 0 2 x - 3 y + 4 z = 0 x + 9 y - z = 0 has infinitely many solutions. Let z = k ∈ R then x = - 11 k 7 ,   y = 2 k 7 ,   z = k Also x 2 + y 2 + z 2 = 1 ∴ k = ± 7 174 ∴ Two solutions are only possible. Hence, set A contains exactly two elements.