If P(6,10,10),Q(1,0,-5),R(6,-10,`lamda`) are vertices of a triangle right angled at Q, then value of `lamda` is . .

Options

A. 0
B. 1
C. 3
D. 2

Answer

A

Explanation

In `DeltaPQR` is right angled, at `theta`
`thereforePR^(2)=PQ^(2)+RQ^(2)`
`implies(6-6)^(2)+(-10-10)^(2)+(lamda-10)^(2)+[(1-6)^(2)+(0-10)^(2)+(-5-10)^(2)]`
`=[(1-6)^(2)+(0+10)^(2)+(-5-lamda)^(2)]`
`implies400+lamda^(2)+100-20lamda=(25+100+225)+(25+100+25+lamda^(2)+10lamda)`
`implieslamda^(2)-20lamda+500=350+150+10lamda+lamda^(2)`
`implies-20lamda=10lamdaimplies30lamda=0implieslamda=0`