Question

Vector a = 3i + mj, vector b = 2i - nj and vector c = ni + 8j. If a and b is perpendicular to each other and b and c are parallel to each other, find m and n.

Answer 1

May be you know it or not a two dimensional vector can be represented by a complex number.Why i have written this statement you will just know when you will see its solution

a = 3i + mj and  b = 2i - nj are perpendicular to each other ,so their dot product

will be zero.

$i.e a.b = 0\\(3i + mj) .(2i - nj)=0\\6-mn=0\\mn=6$j

vector b = 2i - nj and vector c = ni + 8j are parallel to each other.$2i - nj = k (ni + 8j)2/n = -n/8n^{2} =-16n=4i$j

mn = 6

so m=6/4i

m=3/2i

m=3i^{4}/2i

m = 3i^{3}/2

m= -3i/2 as(i^{4} =1, i^{3} = -i[/tex][/tex]