The unit vector which is orthogonal to the vector a- - 3 i- - 2 j- - 6 k- and is coplanar with the vectors b- - 2 i- - j- - k- and c- - i- - j- - k- is

The correct option is A 3 j⃗ k⃗√(10) Vector co planer of b⃗ and c⃗ is given by, p⃗ = b⃗+λc⃗ = 2î+ĵ+k̂+λ(î ĵ+k̂)=(2+λ)î+(1 λ)ĵ+(1+λ)k̂ A ...

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Applications of Dot Product

The unit vect...

Question

The unit vector which is orthogonal to the vector $\to a = 3 \to i + 2 \to j + 6 \to k$ and is coplanar with the vectors $\to b = 2 \to i + \to j + \to k$ and $\to c = \to i - \to j + \to k$ is

\frac{1}{\sqrt{41}} (2 \to i - 6 \to j + \to k)

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\frac{2 \to i - 3 \to j}{\sqrt{13}}

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\frac{3 \to j - \to k}{\sqrt{10}}

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\frac{4 \to i + 3 \to j - 3 \to k}{\sqrt{14}}

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\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 r = 3 \to i + 2 \to j - 5 \to k

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

\to b = \to i + 3 \to j - 2 \to k

\to c = - 2 \to i + \to j - 3 \to k

\to r = λ \to a + μ \to b + ν \to c

\to A = 2 \to i + \to k, \to B = \to i + \to j + \to k,

\to C = 4 \to i - 3 \to j + 7 \to k

\to R

\to R \times \to B = \to C \times \to B

\to R . \to A = 0

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

\to b = 2 \to i + 3 \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

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