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સદિશ બીજગણિત — ગણિત ધોરણ 12 સાયન્સ — Question

Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિતસદિશ બીજગણિત1 Mark
MCQ
જો સદીશો $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ માટે $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$ તથા $|\overrightarrow{a}|=1,|\overrightarrow{b}|=2,|\overrightarrow{c}|=3,$ તો $\overrightarrow{a}\cdot\overrightarrow{b}+\overrightarrow{b}\cdot\overrightarrow{c}+\overrightarrow{c}\cdot\overrightarrow{a}=\ ........ $
  • A
    $-5$
  • B
    $-4$
  • ✓
    $-7$
  • D
    $-4$
✓

Answer

Correct option: C.
$-7$
$|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|^2=|\overrightarrow{a}|^2+|\overrightarrow{b}|^2+|\overrightarrow{c}|^2+2(\overrightarrow{a}\cdot\overrightarrow{b}+\overrightarrow{b}\cdot\overrightarrow{c}+\overrightarrow{c}\cdot\overrightarrow{a})$
$\therefore {0}=1+4+9+2(\overrightarrow{a}\cdot\overrightarrow{b}+\overrightarrow{b}\cdot\overrightarrow{c}+\overrightarrow{c}\cdot\overrightarrow{a})$
$\therefore \overrightarrow{a}\cdot\overrightarrow{b}+\overrightarrow{b}\cdot\overrightarrow{c}+\overrightarrow{c}\cdot\overrightarrow{a}=-7$

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