If b c are any two perpendicular unit vectors and a is any vector, then, ( a b ) b +( a c…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If \(\overrightarrow{\mathrm{b}} \& \overrightarrow{\mathrm{c}}\) are any two perpendicular unit vectors and \(\stackrel{\rightharpoonup}{\mathrm{a}}\) is any vector, then, \((\vec{a} \cdot \vec{b}) \vec{b}+(\vec{a} \cdot \vec{c}) \vec{c}+\frac{\vec{a} \cdot(\vec{b} \times \vec{c})}{|\vec{b} \times \vec{c}|^{2}}(\vec{b} \times \vec{c})\)is equal to :
- \(\stackrel{\rightharpoonup}{\mathrm{a}}\)
- \(\overrightarrow{\mathrm{b}}\)
- \(\stackrel{\rightharpoonup}{\mathrm{c}}\)
- none of these
Answer
(A) a
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