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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
If $\bar{a}, \bar{b}, \bar{c}$ are non-zero vectors such that $\overline{ a } \cdot \overline{ b }=\overline{ a } \cdot \overline{ c }$, then which statement is true?
  • A
    $\overline{ b }=\overline{ c }$
  • B
    $\bar{a} \perp(\bar{b}-\bar{c})$
  • ✓
    $\bar{b}=\bar{c}$ or $\bar{a} \perp(\bar{b}-\bar{c})$
  • D
    None of these
✓

Answer

Correct option: C.
$\bar{b}=\bar{c}$ or $\bar{a} \perp(\bar{b}-\bar{c})$
(C) $\overline{ a } \cdot \overline{ b }=\overline{ a } \cdot \overline{ c }$
$\begin{array}{l}\Rightarrow \overline{ a } \cdot \overline{ b }-\overline{ a } \cdot \overline{ c }=0 \\ \Rightarrow \overline{ a } \cdot(\overline{ b }-\overline{ c })=0 \\ \Rightarrow \text { Either } \overline{ b }-\overline{ c }=0 \text { or } \overline{ a }=0 \\ \Rightarrow \overline{b}=\overline{ c } \text { or } \overline{ a } \perp(\overline{ b }-\overline{ c })\end{array}$

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