The unit vector perpendicular to both ...

CBSE Class 12 Math 2024 All Sets Solved Paper

Question : 15 of 20

Marks: +1, -0

The unit vector perpendicular to both vectors

\hat{i} + \hat{k}

and

\hat{i} - \hat{k}

Solution:

Formula to be used:

\vec{n} = \vec{a} \times \vec{b}

and

\hat{n} = \frac{\vec{n}}{\vec{|n|}}

where it is the unit vector perpendicular to both vectors

\vec{a}

and

\vec{b}

\vec{n} = (\hat{i} + \hat{k}) \times (\hat{i} - \hat{k}) = \hat{\begin{vmatrix} i & \hat{j} & \hat{k} \\ 1 & 0 & 1 \\ 1 & 0 & -1 \end{vmatrix}} = -\hat{j}(-1-1) = 2\hat{j}

\hat{n} = \frac{\hat{2j}}{2} = \hat{j}

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