Let u→=i^+j^,v→=i^−j^,w→=i^+2j^+3k^ If n^ is a unit vector such that u→⋅n^=0 and v→⋅n^=0 then |w→⋅n^|=

u→⋅n^=0,v→⋅n^=0⇒n^ is along u→×v→=i^j^k^1101−10=−2k∴n^=±k (unit vector)w→⋅n^=(i^+2j^+3k^)⋅(±k^)=±3⇒|w→⋅n^|=3.

Let u→=i^+j^,v→=i^−j^,w→=i^+2j^+3k^ If n^ is a unit vector such that u→⋅n^=0 and v→⋅n^=0 then |w→⋅n^|=

u→⋅n^=0,v→⋅n^=0⇒n^ is along u→×v→=i^j^k^1101−10=−2k∴n^=±k (unit vector)w→⋅n^=(i^+2j^+3k^)⋅(±k^)=±3⇒|w→⋅n^|=3.

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Let $\vec{u} = \hat{i} + \hat{j}, \vec{v} = \hat{i} - \hat{j}, \vec{w} = \hat{i} + 2 \hat{j} + 3 \hat{k}$ If $\hat{n}$ is a unit vector such that $\vec{u} \cdot \hat{n} = 0$ and $\vec{v} \cdot \hat{n} = 0$ then $| \vec{w} \cdot \hat{n} | =$

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$\vec{u} \cdot \hat{n} = 0, \vec{v} \cdot \hat{n} = 0 \Rightarrow \hat{n}$ is along $\vec{u} \times \vec{v}$

$= |\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 0 \\ 1 & - 1 & 0 \end{array}| = - 2 k ∴ \hat{n} = \pm k$ (unit vector)

$\vec{w} \cdot \hat{n} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) \cdot (\pm \hat{k}) = \pm 3 \Rightarrow | \vec{w} \cdot \hat{n} | = 3 .$

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Let u→=i^+j^,v→=i^−j^,w→=i^+2j^+3k^ If n^ is a unit vector such that u→⋅n^=0 and v→⋅n^=0 then |w→⋅n^|=

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Let $\vec{u} = \hat{i} + \hat{j}, \vec{v} = \hat{i} - \hat{j}, \vec{w} = \hat{i} + 2 \hat{j} + 3 \hat{k}$ If $\hat{n}$ is a unit vector such that $\vec{u} \cdot \hat{n} = 0$ and $\vec{v} \cdot \hat{n} = 0$ then $| \vec{w} \cdot \hat{n} | =$