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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?

Answer»

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Solution :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))`


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