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Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
Choose the correct answer from the given four options. Projection vector of $\vec{\text{a}}$ on $\vec{\text{b}}$ is:
  • ✓
    $\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|^2}\bigg)\vec{\text{b}}$
  • B
    $\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|}$
  • C
    $\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{a}}|}$
  • D
    $\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{a}}|^2}\bigg)\vec{\text{b}}$
✓

Answer

Correct option: A.
$\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|^2}\bigg)\vec{\text{b}}$
Projection vector of $\vec{\text{a}}$ on $\vec{\text{b}}$ is given by $\vec{\text{a}}\cdot\frac{\vec{\text{b}}}{|\vec{\text{b}}|}\vec{\text{b}}=\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|^2}\bigg)\vec{\text{b}}$

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