Practicing Success
In Figure, if the coordinates of P are (a, b, c), then the perpendicular distances of P from the coordinates axes are respectively |
$\sqrt{a^2 + b^2 }, \sqrt{b^2+c^2}, \sqrt{c^2+a^2}$ $\sqrt{b^2 + c^2 }, \sqrt{c^2+a^2}, \sqrt{a^2+b^2}$ $\sqrt{c^2 + a^2 }, \sqrt{a^2+b^2}, \sqrt{b^2+c^2}$ a, b, c |
$\sqrt{b^2 + c^2 }, \sqrt{c^2+a^2}, \sqrt{a^2+b^2}$ |
PA, PB and PC are the perpendicular distances of point P from OX, OY and OZ respectively. In right angled triangle ADP, we have $AP^2 = AD^2 +DP^2 $ $⇒ PA = \sqrt{AD^2 +DP^2 }$ $⇒ PA = \sqrt{b^2 +c^2} $ $[∵ AD = OB = b $ and $PD = OC = c]$ In right angles triangle PDB right angled at D, we have $PB^2 = BD^2 +PD^2 $ $⇒PB = \sqrt{BD^2 +PD^2} $ $⇒PB = \sqrt{a^2 +c^2} $ $[∵BD = OA = a $ and $ PD = OC = c]$ In right angled triangle PCF right angled at F, we have $PC^2 = PF^2 +CF^2 $ $⇒ PC = \sqrt{PF^2+CF^2}$ $⇒ PC = \sqrt{b^2+a^2}$ $[∵ PF = AD = OB = b $ and $ CF = OA = a]$ $⇒ PC = \sqrt{a^2+b^2}$ |