a, b are the magnitudes of vectors. If  $\overrightarrow{a}\times \overrightarrow{b}=0$, then the value of $\overrightarrow{a}.\overrightarrow{b}$ is

$$\begin{gathered} \text{ Given that, }\left|\overrightarrow{a}\right|=a\text{ and }\left|\overrightarrow{b}\right|=b \\ \text{ Also given that }\overrightarrow{a}\text{×}\overrightarrow{b}=0 \\ \left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\sin \theta =0\text{ where }\theta \text{ is the angle between }\overrightarrow{a}\text{ and }\overrightarrow{b}\text{. } \\ \begin{array}{c}\sin \theta =0\\ \theta =0\end{array} \\ \text{ We have to find }\overrightarrow{a}\cdot \overrightarrow{b} \\ \begin{array}{r}\overrightarrow{a}\cdot \overrightarrow{b}=|\overrightarrow{a}\parallel \overrightarrow{b}|\cos \theta \\ =ab\cos 0\\ \overrightarrow{a}\cdot \overrightarrow{b}=ab\end{array} \end{gathered}$$