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Question
Write the number of vectors of unit length perpendicular to both the vectors \[\vec{a} = 2 \hat{ i } + \hat{ j } + 2 \hat{ k } \text{ and } \vec{b} = \hat{ j } + \hat{ k } \] .
Solution
Unit vectors perpendicular to \[\vec{a}\] and \[\vec{b}\] are \[\pm \left( \frac{\vec{a} \times \vec{b}}{\left| \vec{a} \times \vec{b} \right|} \right)\] .
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