By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2024 Maths, question 25

Topic: Matrices and determinants

Q25

If a,b,ca,b,c are the sides of triangle ABCABC, then what is

∣a2bsin⁡Acsin⁡Absin⁡A1cos⁡Acsin⁡Acos⁡A1∣\left| \begin{matrix} a^{2} & b\sin A & c\sin A \\ b\sin A & 1 & \cos A \\ c\sin A & \cos A & 1 \end{matrix} \right|

equal to ?

  1. (a) ZeroCorrect answer
  2. (b) Area of triangle
  3. (c) Perimeter of triangle
  4. (d) a2+b2+c2a^{2}+b^{2}+c^{2}

Solution.

Answer: (a) Zero

  1. Expanding the determinant gives sin²A[a²−b²−c²+2bc cos A].
  2. The cosine rule says a²=b²+c²−2bc cos A, making the bracket zero.
  3. Thus the determinant is zero.