JEE Advance - Mathematics (1988 - No. 5)
The components of a vector $$\overrightarrow a $$ along and perpendicular to a non-zero vector $$\overrightarrow b $$ are ......and .....respectively.
$$\left( {\frac{{\overrightarrow {a,} .\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow b \,\,\text{and}\,\,\overrightarrow a - \left( {\frac{{\overrightarrow a \,.\,\overrightarrow b }}{{\left| {\overrightarrow b } \right|}}} \right)\overrightarrow b $$
$$\left( {\frac{{\overrightarrow {a,} .\,\overrightarrow b }}{{\left| {\overrightarrow b } \right|}}} \right)\overrightarrow b \,\,\text{and}\,\,\overrightarrow a - \left( {\frac{{\overrightarrow a \,.\,\overrightarrow b }}{{\left| {\overrightarrow b } \right|}}} \right)\overrightarrow b $$
$$\left( {\frac{{\overrightarrow {a,} .\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow b \,\,\text{and}\,\,\overrightarrow a - \left( {\frac{{\overrightarrow a \,.\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow b $$
$$\left( {\frac{{\overrightarrow {a,} .\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow a \,\,\text{and}\,\,\overrightarrow a - \left( {\frac{{\overrightarrow a \,.\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow b $$
$$\left( {\frac{{\overrightarrow {a,} .\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow b \,\,\text{and}\,\,\overrightarrow a + \left( {\frac{{\overrightarrow a \,.\,\overrightarrow b }}{{{{\left| {\overrightarrow b } \right|}^2}}}} \right)\overrightarrow b $$