Let a = i + j + k and b = i + 2j + 3k then a unit vector perpendicular to both vectors (a + b) and (a - b) is equal to Option 1: 1sqrt(6)(-i + 2j - k) Option 2: 1sqrt(6)(i - 2j - k) Option 3: 1sqrt(3)(i + j + k) Option 4: 1sqrt(6)(i + 2j + k)

The answer is '1sqrt(6)(-i + 2j - k)'. View full solution:

Algebra > Vector Algebra

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Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{2j} + 3\hat{k}$ then a unit vector perpendicular to both vectors $(\vec{a} + \vec{b})$ and $(\vec{a} - \vec{b})$ is equal to

$\frac{1}{\sqrt{6}}(-\hat{i} + 2\hat{j} - \hat{k})$

$\frac{1}{\sqrt{6}}(\hat{i} - 2\hat{j} - \hat{k})$

$\frac{1}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k})$

$\frac{1}{\sqrt{6}}(\hat{i} + 2\hat{j} + \hat{k})$

✅ Correct Option: 1

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