Question

find unit vector perpendicular to A =2 i +j + k and B = i-j+2k.

Answer 1

We Know that, vector perpendicular to the two vectors would be given by the cross product of the two.

Unit vector, C = A * B

thus,

C  = (2i + j + k) X (i - j + 2k)
 = i(2+1) - j(4-1) + k(-2-1)
= 3i - 3j - 3k
now, the unit vector would be

C  = C/ |C| = (3i - 3j - 3k) / [32 + 32 + 32] 
=  (3i - 3j - 3k) / √[27]

thus, the unit vector will be

C = (i - j - k) / √3
= i/√3 , -j/√3 , -k/√3 Ans....