The projection vector of on is

Projection vector of a on b is given by = a | b| b = ( a | b| ) b

Vector Algebra — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.No.30,Page.218

Question

The projection vector of $\overrightarrow {\rm{a}}$ on $\overrightarrow {\rm{b}}$ is

(a) $\left( {\frac{{\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} }}{{|\overrightarrow {\rm{b}} |}}} \right)\overrightarrow {\rm{b}}$ ✓ Correct
(b) $\frac{{\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} }}{{|\overrightarrow {\rm{b}} |}}$
(c) $\frac{{\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} }}{{|\overrightarrow {\rm{a}} |}}$
(d) $\left( {\frac{{\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} }}{{|\overrightarrow {\rm{a}} {|^2}}}} \right)\widehat {\rm{b}}$

Step-by-step Solution

Projection vector of $\vec a$ on $\vec b$ is given by $= \vec a \cdot \frac{{\vec b}}{{|\vec b|}}\vec b$

$= \left( {\vec a \cdot \frac{{\vec b}}{{|\vec b|}}} \right) \cdot \vec b$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.