the unit vector is perpendicular to two vectors 3icap + jcap + 2kcap and 2icap – 2jcap + 4kcap is

Dear Student


The vector perpendicular to the two vectors would be givenby cross product of two
A=3i+j+2k
B=2i-2j+4k

Unit vectorperpendicular to the two vectors would be givenby= AxB / IAXBI

AxB= i j k
3 1 2
2 -2 4

=i(8)-j(12-4)+k(-6-2)

=8i-8j-8k

A X B = 8[i – j –k]

IAxBI = √[8²+(-8)²+(-8)²
=√3 [8]²
=8√3

Now unit vector perpendicular to given two vectors = 8[i-j-k] / 8√3
=[ i – j – k ] / √3



Thanks