Let a-3-2-2k- b-2-2k- Then a unit vector perpendicular to both a-b- and a-b- is -

The correct option is A 13( 2î+2ĵ+k̂) We have, a⃗ =3î +2ĵ +2k̂ , b⃗ =î +2ĵ 2k̂ #160; a⃗ +b⃗ =4î +4ĵ â b̂ =2î +4k̂ #160; d⃗ =( a ...

Let a⃗=3î+2...

Question

Let $\to a = 3^i + 2^j + 2^k, b =^i + 2^j - 2^k$ . Then a unit vector perpendicular to both $\to a - \to b$ and $\to a + \to b$ is :

\frac{- 1}{3} (- 2^i + 2^j +^k)

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\frac{1}{3} (- 2^i + 2^j -^k)

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\frac{1}{3} (2^i - 2^j +^k)

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\frac{1}{3} (^i +^j +^k)

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Solution

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

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

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

\to a + 2 \to b - 3 \to c

\sqrt{78}

\to a = 2^i +^j + 3^k

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

\to c =^i -^j - 4^k

\to d =^i + 2^j -^k

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

\to a = 3^i - 2^j +^k, \to b = 2^i - 4^j - 3^k

\to c = - 1^i + 2^j + 2^k

\to a + \to b + \to c =

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

[\to a \to b \to c] .

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

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

\to c = 3^i +^j + 2^k .