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UPSC NDA I 2023 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow :

Let

\vec{a}=3\hat{i}+3\hat{j}+3\hat{k}

and

\vec{c}=\hat{j}-\hat{k}

. Let

\vec{b}

be such that

\vec{a}\cdot\vec{b}=27

and

\vec{a}\times\vec{b}=\overrightarrow{9c}

[NDA I 2023]

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Question : 66 of 120

Marks: +1, -0

What is the angle between

(\vec{a}+\vec{b})

\vec{c}

$\;\frac{\pi}{2}$
$\;\frac{\pi}{3}$
$\;\frac{\pi}{4}$
$\;\frac{\pi}{6}$

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