Question 57

Let $$\overrightarrow{a} = -\hat{i} - \hat{k}, \overrightarrow{b} = -\hat{i} + \hat{k}$$ and $$\overrightarrow{c} = \hat{i} + 2\hat{j} + 3\hat{k}$$ be three given vectors. If $$\overrightarrow{r}$$ is a vector such that $$\overrightarrow{r} \times \overrightarrow{b} = \overrightarrow{c} \times \overrightarrow{b}$$ and $$\overrightarrow{r} . \overrightarrow{a} = 0$$, then the value of $$\overrightarrow{r} . \overrightarrow{b}$$ is


Correct Answer: 9


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