NIMCET 2020 Question Paper with solutions

Question : 36 of 120

Marks: +1, -0

Vertices of the vectors

i-2j+2k, 2i+j-k

and

3i-j+2k

form a triangle. This triangle is

Solution:

a↖{→}=(1,-2,2),b↖{→}=(2,1,-1),c↖{→}=(3,-1,2)

{AB}↖{→}=b↖{→}-a↖{→}=(2,1,-1)-(1,-2,2)=(1,3,-3)⇒|{AB}↖{→}|=√19

{BC}↖{→}=c↖{→}-b↖{→}=(3,-1,2)-(2,1,-1)=(1,-2,3)⇒|{BC}↖{→}|=√14

{CA}↖{→}=a↖{→}-c↖{→}=(1,-2,2)-(3,-1,2)=(-2,-1,0)⇒|{CA}↖{→}|=√5

|{BC}↖{→}|+|{CA}↖{→}|^2=|{AB}↖{→}|^2

14+5=19

Therefore right angle triangle

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