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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
$A, B, C, D, E $ are five coplanar points, then $\overrightarrow {DA} + \overrightarrow {DB} + \overrightarrow {DC} + \overrightarrow {AE} + \overrightarrow {BE} + \overrightarrow {CE} $ is equal to
  • A
    $\overrightarrow {DE} $
  • ✓
    $3\,\overrightarrow {DE} $
  • C
    $2\,\overrightarrow {DE} $
  • D
    $4\,\overrightarrow {ED} $
✓

Answer

Correct option: B.
$3\,\overrightarrow {DE} $
b
(b) $A,\,B,\,C,\,D,\,E$ are five co-planar points.

$\overrightarrow {DA} + \overrightarrow {DB} + \overrightarrow {DC} + \overrightarrow {AE} + \overrightarrow {BE} + \overrightarrow {CE} $

=$(\overrightarrow {DA} + \overrightarrow {AE} ) + (\overrightarrow {DB} + \overrightarrow {BE} ) + (\overrightarrow {DC} + \overrightarrow {CE} )$

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

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