TS EAMCET · Maths · Vector Algebra
If the volume of a tetrahedron having \(\bar{i}+2 \bar{j}-3 \bar{k}, 2 \bar{i}+\bar{j}-3 \bar{k}\) and \(3 \bar{i}-\bar{j}+\mathrm{p} \bar{k}\) as its coterminous edges is 2, then the values of \(p\) are the roots of the equation
- A \(x^2+4 x-12=0\)
- B \(x^2+8 x+12=0\)
- C \(x^2-4 x-12=0\)
- D \(x^2-8 x+12=0\)
Answer & Solution
Correct Answer
(A) \(x^2+4 x-12=0\)
Step-by-step Solution
Detailed explanation
\(V = \frac{1}{6} | \begin{vmatrix} a_x & a_y & a_z \\ b_x & b_y & b_z \\ c_x & c_y & c_z \end{vmatrix} |\) \(2 = \frac{1}{6} | \begin{vmatrix} 1 & 2 & -3 \\ 2 & 1 & -3 \\ 3 & -1 & p \end{vmatrix} |\) \(12 = |1(p-3) - 2(2p+9) - 3(-2-3)|\) \(12 = |p-3-4p-18+15|\) \(12 = |-3p-6|\)…
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