Find a unit vector perpendicular to both the vectors 3- - -2k- and B -2- -2- -4k-

A vector perpendicular to both #160; A⃗ and #160; B⃗ is #160; A⃗×B⃗ . A⃗×B⃗ = #160; (3î ĵ+2k̂)× (2î 2ĵ+4k̂) #160; #160; ...

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Byju's Answer

Standard XII

Physics

Acceleration in 2D

Find a unit v...

Question

Find a unit vector perpendicular to both the vectors $3^i -^j + 2^k$ and $\to B = 2^i - 2^j + 4^k$

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Solution

A vector perpendicular to both $\to A$ and $\to B$ is $\to A \times \to B$ .
$\to A \times \to B$ = $(3^i -^j + 2^k) \times (2^i - 2^j + 4^k)$
= $(- 8^j - 4^k)$
Therefore , a unit vector perpendicular to both $\to A$ and $\to B$
is $\pm$ $\frac{\to A \times \to B}{∣ ∣ \to A \times \to B ∣ ∣}$
= $\pm \frac{(- 8^j - 4^k)}{\sqrt{80}}$

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Find a unit vector perpendicular to both the vectors 3^i−^j+2^k and →B=2^i−2^j+4^k

A vector perpendicular to both →A and →B is →A×→B .→A×→B = (3^i−^j+2^k)×(2^i−2^j+4^k) = (−8^j−4^k)Therefore , a unit vector perpendicular to both →A and →Bis ±→A×→B∣∣→A×→B∣∣= ±(−8^j−4^k)√80

Find a unit vector perpendicular to both the vectors $3^i -^j + 2^k$ and $\to B = 2^i - 2^j + 4^k$