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Show that the vectors a =3hati - 2hatj+h...

Show that the vectors `a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk` and `c=2hatj+hatj-4hatk` form a right angled triangle.

A

an equilateral triangle

B

isosceles triangle

C

a right angled triangle

D

no triangle

Text Solution

Verified by Experts

The correct Answer is:
C
`vecA=3hati-2hatj+hatk,vecB=hati-3hatj+5hatk,vecC=2hati-hatj+4hatk`
`|vecA|=sqrt(3^(2)+(-2)^(2)+1^(2))=sqrt(9+4+1)=sqrt(14)`
`|vecB|=sqrt(1^(2)+(-3)^(2)+5^(2))=sqrt(1+9+25)=sqrt(35)`
`|vecA|=sqrt(2^(2)+1^(2)+(-4)^(2))=sqrt(4+1+16)=sqrt(21)`
As `B=sqrt(A^(2)+C^(2))` therefore ABC will be right angled tgriangle.
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