Let $\overrightarrow{\mathrm{a}}=2\hat{\mathrm{i}}-7\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ , $\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\widehat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\widehat{\mathrm{k}}$ be three given vectors. If $\overrightarrow{\mathrm{r}}$ is a vector such that $\overrightarrow{\mathrm{r}} imes\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{c}} imes\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{r}}\cdot\overrightarrow{\mathrm{b}}=0$, then $\left|\overrightarrow{\mathrm{r}} ight|$ is equal to:

Question

Let $\overrightarrow{\mathrm{a}}=2\hat{\mathrm{i}}-7\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ , $\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\widehat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\widehat{\mathrm{k}}$ be three given vectors. If $\overrightarrow{\mathrm{r}}$ is a vector such that $\overrightarrow{\mathrm{r}}	imes\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{c}}	imes\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{r}}\cdot\overrightarrow{\mathrm{b}}=0$, then $\left|\overrightarrow{\mathrm{r}}ight|$ is equal to:

Dr. Abubacker · Accepted Answer

The correct answer is Option A: $\frac{11}{7}\sqrt{2}$.

Explanation

Reviewed by Dr. Abubacker

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