If = i -3 j , = i +2 j - k , then express in the form = ₁+ ₂ where ₁ is parallel to and ₂ is perpendicular to , then ₁ is given by

Step-by-step solution

Given = i -3 j , = i +2 j - k = ₁+ ₂ ₁ is parallel to aligned ₁ & = ₁= i -3 j Also, & = ₁+ ₂ ₂ & = - ₁=( i +2 j - k )-( i -3 j ) ₂ & =(1- ) i +(2-3 ) j - k aligned It is given ₂ is perpendicular to . array cc (1- )(1)+(2+3 )(-3)+(-1)(0)=0 & 1- -6-9 +0=0 & -5-10 =0 & =- 1 2 ₁= -1 2 i + 3 2 j array