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Questions  >>  CBSE XII  >>  Math  >>  Vector Algebra
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Q)

If $|\overrightarrow{a}| = 11, |\overrightarrow {b} | = 23 and |\overrightarrow {a} - \overrightarrow {b} |= 30 $


$(A)\; 40$
$(B)\; 400$
$(C) \; 20$
$(D)\; 200$

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A)
$\begin{align*}|\overrightarrow {a} + \overrightarrow {b}|^2 + |\overrightarrow {a} - \overrightarrow {b}|^2 & = 2 (|a|^2 + |b|^2) \\ & = 2 (121 + 529) \\ & = 2 \times 650 = 1300\end{align*}$
$\implies |\overrightarrow {a} + \overrightarrow {b}| ^2 + (30 \times 30) = 1300$
$\implies \begin{align*} |\overrightarrow {a} + \overrightarrow{b}| ^2 &= 1300 - 900 \\ & = 400 \\ \implies |\overrightarrow {a} + \overrightarrow {b}| & = 20\end{align*}$
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