Question

If \[ \vec a=2\hat i+3\mu\hat j-\hat k, \qquad \vec b=\mu\hat i-2\hat j+3\hat k, \qquad \vec c=\hat i+3\hat j-2\mu\hat k \] are three vectors such that \[ \alpha\vec a+\beta\vec b+\gamma\vec c=\vec 0 \] only when \[ \alpha=\beta=\gamma=0, \] then the set of all real values of \(\mu\) is

• A. \(\mathbb{R}-\left\{9,1,-\frac76\right\}\)
• B. \(\mathbb{R}-\{1\}\)
• C. \(\mathbb{R}-\left\{1,-\frac53\right\}\)
• D. \(\mathbb{R}-\{0\}\)

Hint:

Three vectors in \(\mathbb R^3\) are linearly independent if and only if the determinant formed by their components is non-zero.

Answer 1

The Correct Option is B