If a vector a is expressed as the sum of two vectors a ^ and a ^ along and perpendicular…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If a vector \(\stackrel{\rightharpoonup}{\mathrm{a}}\) is expressed as the sum of two vectors \(\overrightarrow{\mathrm{a}}^{\prime}\) and \(\overrightarrow{\mathrm{a}^{\prime \prime}}\) along and perpendicular to a given vector \(\overrightarrow{\mathrm{b}}\) then \(\overrightarrow{\mathrm{a}^{\prime \prime}}\) is
- \(\frac{(\vec{a} \times \vec{b}) \times \vec{b}}{\vec{b}}\)
- \[\frac{\overrightarrow{\mathrm{b}} \times(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})}{|\overrightarrow{\mathrm{b}}|^{2}}\]
- \(\frac{\overrightarrow{\mathrm{b}} \times(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})}{\overrightarrow{\mathrm{b}}}\)
- \[\frac{\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}}{|\overrightarrow{\mathrm{~b}}|^{2}} \overrightarrow{\mathrm{~b}}\]
Answer
(B) b ( a b ) | b |^ 2
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