The adjacent sides of a parallelogram are 2i-4j-5k- and i-2j-3k- then the unit vector parallel to a diagonal is

The correct option is B 3i⃗ +6j⃗ 2k⃗ 7 Diagonal vector = ( 2î + 4ĵ 5k̂) + ( i + 2ĵ + 3k̂) =3î + 6ĵ 2k̂ Unit vector parallel to diagonal ...

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Vectors and Its Types

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The adjacent sides of a parallelogram are $2 \to i + 4 \to j - 5 \to k$ and $\to i + 2 \to j + 3 \to k$ then the unit vector parallel to a diagonal is

\frac{- \to i + 2 \to j + 8 \to k}{\sqrt{69}}

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\frac{3 \to i + 6 \to j - 2 \to k}{7}

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\frac{- \to i + 2 \to j - 8 \to k}{\sqrt{69}}

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\frac{- \to i - 2 \to j + 8 \to k}{\sqrt{69}}

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\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 = \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 = (- \to i + 2 \to j + 3 \to k) + t (- 2 \to i + \to j + \to k)

\to r = (2 \to i + 3 \to j + 5 \to k) + s (\to i + 2 \to j + 3 \to k)

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

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

\to i + \to j + \to k

2

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

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

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