Question 1: 12 Marks {Ll} Let H and V he the planes given by: (2} H:lx+5y2Az3=E, V:AX+}F+22+1:U. Determine for which value{s} of )l the planes H and 1? are: (a) orthogonal, (2} {I1} Parallel. (2} {1.2) Find an equation for the plane that passes through the origin (D, D, [I] and is parallel to the (3} plane X+3y' 22: E. {1.3) Find the distance between the point (1 , 2, D} and the plane 3X y + 42 : 2. (3} Question 2: ill} Marks (2.1) Find the components of a unit vector satisfying I? 4:: 3, 1 3:: . (3} {2.2} Show that there are innitelyr man}r vectors in R3 with Euclidean norm 1 whose Euclidean (4} inner product with a: 1,3,5 3. is zero. {2.3) Determine all values oil: so that H :15. 3, 2k, k :1 is orthogonal to I? =:: 2, g, k 3:. (3}