10 In this question all measurements are in centimetres.
A small, thin laser pen is set up with one end at \(A ( 7,2 , - 3 )\) and the other end at \(B ( 9 , - 3 , - 2 )\)
A laser beam travels from \(A\) to \(B\) and continues in a straight line towards a large thin sheet of glass.
The sheet of glass lies within a plane \(\Pi _ { 1 }\) which is modelled by the equation
$$4 x + p y + 5 z = 9$$
where \(p\) is an integer.
10
- The laser beam hits \(\Pi _ { 1 }\) at an acute angle \(\alpha\), where \(\sin \alpha = \frac { \sqrt { 15 } } { 75 }\)
Find the value of \(p\)
10 - A second large sheet of glass lies on the other side of \(\Pi _ { 1 }\)
This second sheet lies within a plane \(\Pi _ { 2 }\) which is modelled by the equation
$$4 x + p y + 5 z = - 5$$
Calculate the distance between the sheets of glass.
10 - The point \(A ( 7,2 , - 3 )\) is reflected in \(\Pi _ { 1 }\)
Find the coordinates of the image of \(A\) after reflection in \(\Pi _ { 1 }\)