Question

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

• A. are linearly dependent
• B. are linearly independent
• C. are coplanar
• D. form an isosceles triangle

Answer 1

The correct option is B are linearly independent

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 not equal to zero, the vectors are linearly independent.