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3D Geometry question

2022 · Shift 1 · Q30
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  2. /JEE Advanced
  3. /Mathematics
  4. /3D Geometry
  5. /2022 · Shift 1 · Q30

3D Geometry question

2022 · Shift 1 · Q30

JEE AdvancedMathematics3D GeometryMultiple correct+4 / −2
Let SSS be the reflection of a point QQQ with respect to the plane given by r⃗=−(t+p)ı^+tȷ^+(1+p)k^\vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k}r=−(t+p)^+t^​+(1+p)k^ where t,pt, pt,p are real parameters and ı^,ȷ^,k^\hat{\imath}, \hat{\jmath}, \hat{k}^,^​,k^ are the unit vectors along the three positive coordinate axes. If the position vectors of QQQ and SSS are 10ı^+15ȷ^+20k^10 \hat{\imath}+15 \hat{\jmath}+20 \hat{k}10^+15^​+20k^ and αı^+βȷ^+γk^\alpha \hat{\imath}+\beta \hat{\jmath}+\gamma \hat{k}α^+β^​+γk^ respectively, then which of the following is/are TRUE ?
  1. A
    3(α+β)=−1013(\alpha+\beta)=-1013(α+β)=−101
  2. B
    3(β+γ)=−713(\beta+\gamma)=-713(β+γ)=−71
  3. C
    3(γ+α)=−863(\gamma+\alpha)=-863(γ+α)=−86
  4. D
    3(α+β+γ)=−1213(\alpha+\beta+\gamma)=-1213(α+β+γ)=−121
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