Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsDeterminantsPractice

If a 1 2 + a 2 2 + a 3 2 = 1 ,   b 1 2 + b 2 2 + b 3 2 = 4 ,   c 1 2 + c 2 2 + c 3 2 = 9 , a 1 b 1 + a 2 b 2 + a 3 b 3 = 0 , a 1 c 1 + a 2 c 2 + a 3 c 3 = 0 , b 1 c 1 + b 2 c 2 + b 3 c 3 = 0 and A = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 , then A 4 is equal to

Options

  1. A36
  2. B49
  3. C1296
  4. D216

Correct answer

C. 1296

Step-by-step solution

A 2 = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 = a 1 2 + a 2 2 + a 3 2 a 1 b 1 + a 2 b 2 + a 3 b 3 a 1 c 1 + a 2 c 2 + a 3 c 3 a 1 b 1 + a 2 b 2 + a 3 b 3 b 1 2 + b 2 2 + b 3 2 b 1 c 1 + b 2 c 2 + b 3 c 3 a 1 c 1 + a 2 c 2 + a 3 c 3 b 1 c 1 + b 2 c 2 + b 3 c 3 c 1 2 + c 2 2 + c 3 2 = 1 0 0 0 4 0 0 0 9 = 36 ⇒ A 4 = 1296

Practice Determinants on Quantrex Academy →

More from Determinants

If the system of linear equations: x+y+z=6 , x+2y+5z=10 , 2x+3y+ z= has infinitely many solutions, then the value of + equals: 2026The sum of all possible values of [0, 2 ] , for which the system of equations : x 3 - 8y - 12z = 0 x 2 + 3y + 3z = 0 x + y + 3z = 0 has a non-trivial solution, is equal to : 2026If f: N Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k N , and _ n=1 ^ k f(n) = 98 , then k is equal to : 2026Consider the system of linear equations in x, y, z : x + 2y + tz = 0 , 6x + y + 5tz = 0 , 3x + t^2 y + f(t) z = 0 , where f: R R is a differentiable function. If this system has in 2026If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+ z= has infinitely many solutions, then the value of + is: 2026If the system of equations x + 5y + 6z = 4 , 2x + 3y + 4z = 7 , x + 6y + az = b has infinitely many solutions, then the point (a, b) lies on the line 2026Let , R be such that the system of linear equations x + 2y + z = 5 2x + y + z = 5 8x + 4y + z = 18 has no solution. Then is equal to : 2026The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b has 2026 Full Determinants list All NTA Abhyas JEE Main PYQs