Question

The vectors $2\overline{i}-3\overline{j}+4\overline{k},\overline{i}-2\overline{j}+3\overline{k}$ and $3\overline{i}+\overline{j}-2\overline{k}$

• A. are linearly dependent
• B. are linearly independent
• C. form sides of a triangle
• D. are coplanar

Answer 1

Answer: (B)

are linearly independent

Finding the determinant of the coefficient matrix:

$\left|\begin{array}{ccc}2& -3& 4\\ 1& -2& 3\\ 3& 1& -2\end{array}\right|=2(4-3)+3(-2-9)+4(1+6)=-3\ne 0$
Since the determinant is $\ne 0$, the vectors are linearly independent.