Hallo like,
ich schreibe Vektor AB = AB ohne Pfeil unt Vektoren in Zeilenschreibweise:
AB = [2, - √2, - √2] , AC = [2, 0, 0]
a)
cos(α) = cos(AB,AC) = AB * AC / ( |AB| * |AC| ) = 1/2
→ α = 60°
AΔ = 1/2 * | AB x AC | = 1/2 * | [2, - √2, - √2] ⨯ [2, 0, 0] | = 1/2 * | [0, - 2·√2, 2·√2] | = 2
b)
Normalenvektor von E = \(\overrightarrow{n}\) = [0, - 2·√2, 2·√2]
Normaleneinheitsvektor \(\overrightarrow{n_0}\) = \(\overrightarrow{n}\) / |\(\overrightarrow{n}\)| = [0, - √2/2, √2/2]
HNF von E: \(\overrightarrow{n_0}\) * \(\overrightarrow{x}\) - \(\overrightarrow{n_0}\) * \(\overrightarrow{a}\) = 0
[0, - √2/2, √2/2] * \(\overrightarrow{x}\) - [0, - √2/2, √2/2] * [0, √2/2, √2/2] = 0
[0, - √2/2, √2/2] * \(\overrightarrow{x}\) = 0
c)
Da E den Nullvektor enthält, ist E ein Untervektorraum von ℝ3
Gruß Wolfgang