How to write the second question of geometry in the picture? Write with vectors. Thank you.

Proof: (1) See the figure below. The black line is the outline of the three-dimensional figure, the blue line is the invisible dotted line, and the red line is the auxiliary line for solving the problem. Connect CE to get: square AECD；; ; Because in the plane ABCD, AB//CD, AB⊥AD, AB=2AD=2DC=6√2, AE = (1/2) AB = AD = DC = CE = 3 √ 2; Connect DE to AC in F, and DE ⊥ AC (DF ⊥ AC, EF ⊥ AC); DE and AC are divided vertically. DF=FE=( 1/2)√2AD=3. Then, the above conclusion will not change regardless of the folding angle when it is folded in half along the AC line. As long as the orthogonal projection G of D falls on the plane ABC, it must be on the extension line of EF or EF. DG⊥ Aircraft abc；; Because AC⊥E(G)F, GF is the projection of DE, so DE⊥AC (triple vertical theorem). Complete the certificate.

(2) solution: because v = (1/3) (1/2) ab * ce * DG = (1/6) 6 √ 2 * 3 √ 2 * DG = 6DG =12 √ 2. ? Get: DG = 2 √ 2;

fg=√(df^2-dg^2)=√[3^2-(2√2)^2]= 1；

Taking the G point as the origin, Gx//AC as the X axis, EF//BD as the Y axis and GD as the Z axis, the spatial rectangular coordinate system O-xyz is established.

Coordinates a (-3, 1, 0) and b (3 3,5,0) of the relevant point; D(0，0，2√2)； F(0， 1，0)；

Vector AF = {3,0,0}, DF={0, 1,-2 √ 2}; BD={-3，5，2√2 }； Let the normal vector of planar DAC be n;

n=AFxDF={3，0，0}x{0， 1，-2√2}={0，6√2，-3 }；

cos(n^bd)=n BD/(| n | * | BD |)=[0 *(-3)+(6√2)* 5+(-3)*(2√2)]/√[(2 * 36+9)*(9+25+8)]

=24√2/(9*√42)=8/(3√2 1)=8√2 1/63。