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STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
Five points given by  $ A, B, C, D, E $ are in a plane. Three forces $\overrightarrow {AC} ,\,\,\overrightarrow {AD} $ and $\overrightarrow {AE} $ act at A and three forces $\overrightarrow {CB} ,\,\,\overrightarrow {DB} ,\,\,\overrightarrow {EB} $ act at $ B$. Then their resultant is
  • A
    $2\overrightarrow {AC} $
  • ✓
    $3\overrightarrow {AB} $
  • C
    $3\overrightarrow {DB} $
  • D
    $2\overrightarrow {BC} $
✓

Answer

Correct option: B.
$3\overrightarrow {AB} $
b
(b) Points $A, B, C, D, E$  are in a plane.

Resultant $ = (\overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} ) + (\overrightarrow {CB} + \overrightarrow {DB} + \overrightarrow {EB} )$

$ = (\overrightarrow {AC} + \overrightarrow {CB} ) + (\overrightarrow {AD} + \overrightarrow {DB} ) + (\overrightarrow {AE} + \overrightarrow {EB} )$

$ = \overrightarrow {AB} + \overrightarrow {AB} + \overrightarrow {AB} = 3\overrightarrow {AB} $.

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