Question

\(\overline{a}, \overline{b}, \overline{c}\) are non-coplanar vectors. If \(\overline{x}=2\overline{a}+3\overline{b}+4\overline{c}\), \(\overline{y}=3\overline{a}+4\overline{b}+5\overline{c}\), \(\overline{z}=4\overline{a}+5\overline{b}+6\overline{c}\), then \([\overline{x}\ \overline{y}\ \overline{z}]=\):

• A. \(>0\)
• B. \(9[\overline{a}\overline{b}\overline{c}]\)
• C. \(15[\overline{a}\overline{b}\overline{c}]\)
• D. \(12[\overline{a}\overline{b}\overline{c}]\)

Hint:

If consecutive rows differ by constant increments, check determinant dependency quickly.

Answer 1

The Correct Option is D