The following system of equations does not have a unique solution

MATHEMATICS · Multi-part · CBSE · Mathematics · Determinants · Determinants

Problem

The following system of equations does not have a unique solution.

\begin{cases} 6x + ky + 2z = a \\ 6x - y - z = 7 \\ 2x - 3y + z = 1 \end{cases}

(1) (a) Find the value of

k

. (2) Each equation represents a plane. (b) Find (i) the value of

a

for which the three planes intersect in a line (ii) the equation of the line. (3) (c) If the value of

a

is such that the three planes do not intersect in a line, describe their geometric configuration, justifying your answer.