Question

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

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

Answer 1

The correct option is B are linearly independent

a set of vectors is said to be linearly dependent if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent.
the condition can be checked by Checking the determinant of $A$

$A=\left[\begin{array}{ccc}2& -3& 1\\ 1& -2& 3\\ 3& 1& -2\end{array}\right]$
if $|A|=0$ then vectors are said to be linearly dependent
if $|A|$ is nonzero then vectors are said to be linearly independent
and on solving $|A|=-24$ which is non zero
So, Answer is $B$