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Scalar Or Dot Product — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSScalar Or Dot Product1 Mark
Question
If $|\vec{\text{a}}|=\big|\vec{\text{b}}\big|,$ then $\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=$
  1. Positive
  2. Negetive
  3. 0
  4. None of these
✓

Answer

  1. 0
Solution:
Given that
$|\vec{\text{a}}|=|\vec{\text{a}}|$
$\Rightarrow\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=|\vec{\text{a}}|^2-\big|\vec{\text{b}}\big|^2$
$|\vec{\text{a}}^2-|\vec{\text{a}}|^2$
$=0$

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