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Question
Let S be the reflection of a point Q with respect to the plane given by
→r=−(t+p)^i+t^j+(1+p)^k
where t,p are real parameters and ^i,^j,^k are the unit vectos along the three positive coordinates axes. If the position vectors of Q and S are 10^i+15^j+20^k and α^i+β^j+γ^k respectively, then which of the following is/are TRUE ?
Let S be the reflection of a point Q with respect to the plane given by
→r=−(t+p)^i+t^j+(1+p)^k
where t,p are real parameters and ^i,^j,^k are the unit vectos along the three positive coordinates axes. If the position vectors of Q and S are 10^i+15^j+20^k and α^i+β^j+γ^k respectively, then which of the following is/are TRUE ?
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Solution
The correct option is D 3(α+β)=−101
Equation of plane is
→r=−(t+p)^i+t^j+(1+p)^k
→r=^k+t(−^i+^j)+p(−^i+^k)
Equation of plane in standard form is
[→r−^k−^i+^j−^i+^k]=0
∴x+y+z=1…(1)
Coordinates of Q=(10,15,20)
Coordinates of S=(α,β,γ)
∴α−101=β−151=γ−201=−2(10+15+20−1)3
∴α−10=β−15=γ−20=−833
∴α=−583,β=−433,γ=−283
∴3(α+β)=−101,3(β+γ)=−71
3(γ+α)=−86 and 3(α+β+γ)=−129
Equation of plane is
→r=−(t+p)^i+t^j+(1+p)^k
→r=^k+t(−^i+^j)+p(−^i+^k)
Equation of plane in standard form is
[→r−^k−^i+^j−^i+^k]=0
∴x+y+z=1…(1)
Coordinates of Q=(10,15,20)
Coordinates of S=(α,β,γ)
∴α−101=β−151=γ−201=−2(10+15+20−1)3
∴α−10=β−15=γ−20=−833
∴α=−583,β=−433,γ=−283
∴3(α+β)=−101,3(β+γ)=−71
3(γ+α)=−86 and 3(α+β+γ)=−129
Suggest Corrections
25
respectively, in the ration 2:1