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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
The orthogonal projection of $\vec{\text{a}}$ on $\vec{\text{b}}$ is:
  1. $\frac{\big(\vec{\text{a}}.\vec{\text{b}}\big)\vec{\text{a}}}{|\vec{\text{a}}|^2}$
  2. $\frac{\big(\vec{\text{a}}.\vec{\text{b}}\big)\vec{\text{b}}}{\big|\vec{\text{b}}\big|^2}$
  3. $\frac{\vec{\text{a}}}{|\vec{\text{a}}|}$
  4. $\frac{\vec{\text{b}}}{\big|\vec{\text{b}}\big|}$
✓

Answer

  1. $\frac{\big(\vec{\text{a}}.\vec{\text{b}}\big)\vec{\text{b}}}{\big|\vec{\text{b}}\big|^2}$

Solution:

The orthogonal projection of $​\vec{\text{a}}$ on $​\vec{\text{b}}$ is

$\frac{\big(\vec{\text{a}}.\vec{\text{b}}\big)\vec{\text{b}}}{\big|\vec{\text{b}}\big|^2}$

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