Question

If $a^2 + b^2 + c^2 = 0$ and $$\begin{vmatrix} b^2+c^2 & ab & ac \\ ab & c^2+a^2 & bc \\ ac & bc & a^2+b^2 \end{vmatrix}=ka^2b^2c^2$$ then k is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

When solving matrix determinants with certain conditions, simplify using matrix properties to identify the constant.

Answer 1

The Correct Option is B

Step 1: Using the Given Equation
We are given that \( a^2 + b^2 + c^2 = 0 \), and we need to evaluate the determinant of the matrix.
Step 2: Simplifying the Determinant
By applying the properties of determinants, we can simplify the expression to evaluate \( k \), and we find that the value of \( k \) is 2.
Step 3: Conclusion
Thus, \( k = 2 \).