What is the value of `lambda` if the triangle whose vertices are `hat(i), hat(j)` and `hat(i)+hat(j)+lambdahat(k)` will be right angled?

Options

A. 2
B. 0
C. -1
D. 1

Answer

B

Explanation

Let us consider triangle ABC. Suppose `hat(i), hat(j) and hat(i)+hat(j)+lambda hat(k)` are the position vector of A, B and C.
Then `vec(AB)=hat(j)-hat(i), vec(AC)=hat(j)+lambda hat(k), vec(BC)=hat(i)+lambda hat(k)`
`|vec(AB)|=sqrt((-1)^(2)+(1)^(2))=sqrt(2)`
`|vec(BC)|=sqrt((1)^(2)+(lambda))^(2))=sqrt(1+lambda^(2)`
`|vec(AC)|=sqrt((1)^(2)+(lambda))^(2)=sqrt(1+lambda^(2))`