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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 2 · Set 3 · Q24
If | a |=2,| b |=3 and a · b =4, then evaluate | a +2 b |.
If $\displaystyle |\vec{a}|=2,|\vec{b}|=3$ and $\displaystyle \vec{a} \cdot \vec{b}=4$, then evaluate $\displaystyle |\vec{a}+2 \vec{b}|$.
Marking-scheme solution
\[\begin{aligned}
& (\vec{a}+2 \vec{b})^{2}=|\vec{a}|^{2}+|2 \vec{b}|^{2}+4 \vec{a} \cdot \vec{b} \\
& =56 \\
& \Rightarrow|\vec{a}+2 \vec{b}|=\sqrt{56}
\end{aligned}
\]
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