Find the value of each of a, b and c.

The equations of three planes are

     $2x - 4y - 3z = 4$

     $- x + 3y + 5z = - 2$

     $3x - 5y - z = 6$.

Find a vector equation of the line of intersection of these three planes.

(a)     use GDC or manual method to find a, b and c     (M1)

obtain $a = 2,{\text{ }}b = - 1,{\text{ }}c = 3$ (in any identifiable form)     A1

[2 marks]

use GDC or manual method to solve second set of equations     (M1)

obtain $x = \frac{{4 - 11t}}{2};{\text{ }}y = \frac{{ - 7t}}{2};{\text{ }}z = t$ (or equivalent)     (A1)

$r = \left( {\begin{array}{*{20}{c}}   2 \\   0 \\   0 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}}   { - 5.5} \\   { - 3.5} \\   1 \end{array}} \right)$ (accept equivalent vector forms)     M1A1

Note: Final A1 requires r = or equivalent.

[4 marks]

Generally well done.

Moderate success here. Some forgot that an equation must have an = sign.