Let P be a point in the first octant, whose image Q in the plane x+y=3 (that is, the line segment PQ is perpendicular to the plane x+y=3 and the…

Question

Let P be a point in the first octant, whose image Q in the plane x+y=3 (that is, the line segment PQ is perpendicular to the plane x+y=3 and the mid-point of PQ lies in the plane x+y=3) lies on the z-axis. Let the distance of P from the x-axis be 5. If R is the image of P in the xy-plane, then the length of PR is ______.

MARKS Content Team · Accepted Answer

Correct answer: 8. Let Pα,β,γ, Q0,0,γ and Rα,β,-γ Now, PQ→∥i^+j^ ⇒-αi^+βj^∥i^+j^ ⇒α=β Also, mid point of PQ lies on the plane ⇒(α)/2+(β)/2=3⇒α+β=6⇒α=3 Now, distance of point P from x-axis is √(β^2+γ^2)=5 ⇒β^2+γ^2=25⇒γ^2=16 As β=α=3 As γ=4 Hence, PR=2γ=8

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