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UPSC NDA I 2014 Mathematics Paper

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For the next two (02) items that follow:

Consider the vectors

\vec{a} = \hat{i} - 2\hat{j} + \hat{k}

and

\vec{b} = 4\hat{i} - 4\hat{j} + 7\hat{k}

[NDA I 2014]

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Question : 70 of 120

Marks: +1, -0

What is the vector perpendicular to both the vectors?

$-10\hat{i} - 3\hat{j} + 4\hat{k}$
$-10\hat{i} + 3\hat{j} + 4\hat{k}$
$10\hat{i} - 3\hat{j} + 4\hat{k}$
None of the above

Solution:

\vec{a} \times \vec{b}

will be perpendicular to both given vectors.

\vec{a} \times \vec{b} = \begin{vmatrix} i & j & k \\ 1 & -2 & 1 \\ 4 & -4 & 7 \end{vmatrix}

= -10\hat{i} - 3\hat{j} + 4\hat{k}

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