A unit vector coplanar with i-j-2k- and i-2j-k- and perpendicular to i-j-k- is

The correct options are A 1√(2) ( j⃗+k⃗ ) D 1√(2) ( j⃗ k⃗ ) Let the required vector be pi⃗ + qj⃗ + rk⃗ According to the condition of coplanarit ...

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Definition of a Determinant

A unit vector...

Question

A unit vector coplanar with $\to i + \to j + 2 \to k$ and $\to i + 2 \to j + \to k$ , and perpendicular to $\to i + \to j + \to k$ , is

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

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

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

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

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Solution

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2 \to i - \to j + 2 \to k

\to i + \to j = \to k

2 \to i + \to j - \to k

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

\to a = \to i - 2 \to j - 3 \to k, \to b = 2 \to i + \to j - \to k, \to c = \to i + 3 \to j - 2 \to k

(\to a \times \to b) \times \to c

\to a = \to i + \to j + \to k, \to a = 2 \to i + \to k, \to c = 2 \to i + \to j + \to k; \to d = \to i + \to j + 2 \to k

(\to a \times \to b) \times (\to c \times \to d) = [\to a \to b \to d] \to c - [\to a \to b \to c] \to d

\to i - \to j + \to k, - \to i + \to j + 2 \to k

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