Choose the correct statement(s)

a)  $\left|\left(\overrightarrow{\text{A}}\times \overrightarrow{B}\right)·\overrightarrow{C}\right|$ represents volume of parallelopiped formed by $\overrightarrow{\text{A}},\overrightarrow{B},\overrightarrow{C}$ as adjacent sides. If $\left|\left(\overrightarrow{\text{A}}\times \overrightarrow{B}\right)·\overrightarrow{C}\right|=0$, it means volume is zero. Hence $\overrightarrow{\text{A}},\overrightarrow{B},\overrightarrow{C}$  are coplanar. Option (a) is correct.
b) $\left|\overrightarrow{\text{A}}\times \overrightarrow{\text{B}}\right|=\left|\overrightarrow{\text{A}}·\overrightarrow{\text{B}}\right|\Rightarrow AB\sin \theta =AB\cos \theta \Rightarrow \tan \theta =1\Rightarrow \theta =45°$ . Option (b) is correct.
c) Direction of $\overrightarrow{\text{A}}\times \overrightarrow{\text{B}}$ is perpendicular to the plane containing $\overrightarrow{\text{A}}\&\overrightarrow{\text{B}}$

  $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\overrightarrow{\text{A}}-\overrightarrow{\text{B}}$ are in the plane of $\overrightarrow{\text{A}}\&\overrightarrow{\text{B}}$. Hence the direction of $\overrightarrow{\text{A}}\times \overrightarrow{\text{B}}$  is perpendicular to directions of $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}\overrightarrow{\text{A}}-\overrightarrow{\text{B}}$. Option (c) is correct.
d)  $\overrightarrow{\text{A}}\times \overrightarrow{\text{B}}=AB\sin \theta \widehat{n},\overrightarrow{\text{B}}\times \overrightarrow{\text{A}}=-AB\sin \theta \widehat{n}$ . Option (d) is correct.