Point lies on the plane and is units from

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry

Problem

Point P(x,y,5)P(x,y,5) lies on the plane x+2y+z=17x+2y+z=17 and is 1010 units from Q(2,1,3)Q(2,1,3). If x>yx>y, determine (x,y)(x,y). (a) (18−8265, 21+4265)\left(\dfrac{18-8\sqrt{26}}{5},\,\dfrac{21+4\sqrt{26}}{5}\right) (b) (18+4295, 21−2295)\left(\dfrac{18+4\sqrt{29}}{5},\,\dfrac{21-2\sqrt{29}}{5}\right) (c) (18+8265, 21−4265)\left(\dfrac{18+8\sqrt{26}}{5},\,\dfrac{21-4\sqrt{26}}{5}\right) (d) (22+8215, −19+4215)\left(\dfrac{22+8\sqrt{21}}{5},\,\dfrac{-19+4\sqrt{21}}{5}\right)

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