The three vector `vec(A) = 3hat(i)-2hat(j)+hat(k), vec(B)= hat(i)-3hat(j)+5hat(k)` and `vec(C )= 2hat(i)+hat(j)-4hat(k)` from

Options

A. An equilateral triangel
B. An isosceles triangle
C. A right angle triangle
D. No triangle

Answer

C

Explanation

`vec(A)= 3hat(i)-2hat(j)+hat(k), vec(B)= hat(i)-3hat(j)+5hat(k), vec(C )= 2hat(i)+hat(j)-4hat(k)`
`|vec(A)|= (3^(2)+(2)^(2)+1^(2))= sqrt(9+4+1)= sqrt(14)`
`|vec(B)|= sqrt(1^(2)+(-3)^(2)+5^(2))= sqrt(1+9+25) = sqrt(35)`
`|vec(C )|= 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 triangle