Question

Find the unit vector perpendicular to both the vectors A=3i-j+2k and B=2i-2j+4k.​

Answer 1

Explanation:

A unit vector perpendicular upon A and B is given by

∣A×B∣

±(A×B)

Here , A = 3i + j + 2K

B = 2i - 2j + 4 k

So, A × B =i(4 + 4) -j(12 - 4) + k(-6 - 2) = 8i - 8j - 8k = 8(i - j - k)

⇒ A × B = 8(i - j - k)

Now, |A × B | = √8^2+(-8)^2+(-8)^2

8

2

+(−8)

2

+(−8)

2

|A ×B| = 8√3 unit

Now, unit vector , n =± 8(i - j - k)/8√3

=±(i - j - k )/√3

✅Hope it helps you ❗