If u -2- -2- -k- and v -6- -3- -2k- the unit vector perpendicular to u and v is-

Water perpendicular to u⃗ amp; v⃗ ⇒ u⃗×v⃗ ⇒î #160; amp; ĵ #160; amp; k̂ #160; 2 amp; 2 amp; 1 6 amp; 3 ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If u =2î +2...

Question

If $\to u = 2^i + 2^j -^k$ and $\to v = 6^i - 3^j + 2^k$ the unit vector perpendicular to $\to u$ and $\to v$ is:

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Solution

water perpendicular to $\to u$ & $\to v \Rightarrow \to u \times \to v$
$\Rightarrow ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 2 & - 1 6 & - 3 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$\Rightarrow^i (4 - 3) -^j (4 + 6) +^k (- 6 - 12)$
$\Rightarrow^i - 10^j - 18^k$
unit water $\Rightarrow (\frac{-^i + 10^j + 18^k}{\sqrt{425}})$

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Similar questions

Q. If

\to A = 2^i + 3^j + 6^k

and

\to B = 3^i - 6^j + 2^k

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Q. Let

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

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If →u=2^i+2^j−^k and →v=6^i−3^j+2^k the unit vector perpendicular to →u and →v is:

water perpendicular to →u & →v ⇒ →u×→v⇒∣∣ ∣ ∣∣^i^j^k22−16−32∣∣ ∣ ∣∣⇒ ^i(4−3)−^j(4+6)+^k(−6−12)⇒ ^i−10^j−18^kunit water ⇒ (−^i+10^j+18^k√425)

If $\to u = 2^i + 2^j -^k$ and $\to v = 6^i - 3^j + 2^k$ the unit vector perpendicular to $\to u$ and $\to v$ is: