Q.
Let P be a point in the first octant, whose image Q 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 ______.
Let P(α,β,γ) Q(0,0,γ) and R(α,β,−γ)
Now, PQ∥i^+j^⇒αi^+βj^∥i^+j^ ⇒α=β
Also, mid-point of PQ lies on the plane ⇒2α+2β=3⇒α+β=6⇒α=3
Now, distance of point P from X-axis is β2+γ2=5 ⇒,β2+γ2=25⇒γ2=16
As β=α=3
As γ=4
Hence, PR=2γ=8