A unit vector coplanar with i-j-3k- and i-3j-k- and perpendicular to i-j-k- is

Let â=xî+yĵ+zk̂ ⇒ x amp; y amp; z 1 amp; 1 amp; 3 1 amp; 3 amp; 1 =0⇒ 4x y z=0 also x+y+z=0 ⇒ x=0 and y= z ∴â=yĵ yk̂ is a unit vector ⇒ y=1 ...

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Test for Collinearity of Vectors

A unit vector...

Question

A unit vector coplanar with $\to i + \to j + 3 \to k and \to i + 3 \to j + \to k$ and perpendicular to $\to i + \to j + \to k$ is

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

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

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$\frac{1}{\sqrt{2}} (\to j - \to k)$

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

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