determine a unit vector perpendicular to both vector a=2i+k and vector b=i-j+2k

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Solution

$W e k n o w c r o s s p r o d u c t o f t w o v e c t o r s g i v e s t h e v e c t o r w h i c h i s p e r p e n d i c u l a r t o b o t h t h e v e c t o r s . \vec{A} = 2 \hat{i} + \hat{k} \vec{B} = \hat{i} - \hat{j} + 2 \hat{k} l e t \vec{C} i s p e r p e n d i c u l a r t o b o t h t h e v e c t o r s . \vec{C} = \vec{A} \times \vec{B} = (2 \hat{i} + \hat{k}) \times (\hat{i} - \hat{j} + 2 \hat{k}) = \hat{i} - 3 \hat{j} - 2 \hat{k}$

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Similar questions

4 \hat{i} - \hat{j} + 3 \hat{k} and - 2 \hat{i} + \hat{j} - 2 \hat{k} .

\vec{a} = 2 \hat{i} + \hat{j} + \hat{k} and \vec{b} = \hat{i} + 2 \hat{j} + \hat{k} .

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

\sqrt{2}

3 i - j - k

i + j - 2 k

2 i + 2 j + k

\to a = 2 ˆ i - ˆ j + 2 ˆ k

\to b = - ˆ i + ˆ j - ˆ k

\to a + \to b

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