JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}, \vec{b}, \vec{c}\) be three vectors mutually perpendicular to each other and have same magnitude. If a vector \(\overrightarrow{\mathrm{r}}\) satisfies. \(\overrightarrow{\mathrm{a}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{a}}\}+\overrightarrow{\mathrm{b}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{c}}) \times \overrightarrow{\mathrm{b}}\}+\overrightarrow{\mathrm{c}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{a}}) \times \overrightarrow{\mathrm{c}}\}=\overrightarrow{0}\) then \(\overrightarrow{\mathrm{r}}\) is equal to:
- A \(\frac{1}{3}(\vec{a}+\vec{b}+\vec{c})\)
- B \(\frac{1}{3}(2 \overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}})\)
- C \(\frac{1}{2}(\vec{a}+\vec{b}+\vec{c})\)
- D \(\frac{1}{2}(\vec{a}+\vec{b}+2 \vec{c})\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}(\vec{a}+\vec{b}+\vec{c})\)
Step-by-step Solution
Detailed explanation
Suppose \(\overrightarrow{\mathrm{r}}=\mathrm{x} \overrightarrow{\mathrm{a}}+\mathrm{yb}+2 \overrightarrow{\mathrm{c}}\) and \(|\overrightarrow{\mathrm{a}}|=|\overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{c}}|=\mathrm{k}\)…
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