Question

If the volume of a tetrahedron having \( \vec{i}+2\vec{j}-3\vec{k} \), \( 2\vec{i}+\vec{j}-3\vec{k} \) and \( 3\vec{i}-\vec{j}+p\vec{k} \) as its coterminous edges is 2, then the values of p are the roots of the equation

• A. \( x^2 + 4x - 12 = 0 \)
• B. \( x^2 + 8x + 12 = 0 \)
• C. \( x^2 - 4x - 12 = 0 \)
• D. \( x^2 - 8x + 12 = 0 \)

Hint:

The volume of a parallelepiped with edges \( \vec{a}, \vec{b}, \vec{c} \) is \( |[\vec{a} \vec{b} \vec{c}]| \). The volume of the tetrahedron formed by the same edges is \( \frac{1}{6} \) of this value. Remember the absolute value, as volume cannot be negative.

Answer 1

The Correct Option is A