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Question : 61 of 90
Marks:
+1,
-0
Solution:
P1:x−y+2z=2 P2=2x+y−3=2
Let line of Intersection of planes
P1 and
P2 cuts
xy plane in point
Q.
⇒ z-coordinate of point
Q is zero
⇒}‌ ⇒x=,y= ⇒Q(,,0) Vector parallel to the line of intersection
=|| =−+5+3 Equation of Line of intersection
===λ( say
) Let coordinates of foot of perpendicular be
F(−λ+,5λ−,3λ) =(−λ+)+(5λ−)+(3λ) .=0 ⇒λ−+25λ+9λ=0 ⇒35λ=⇒λ= Now,
α=−λ+,β=5λ−,γ=3λ ⇒α+β+γ=7λ+ =7()+ = ⇒35(α+β+γ)=×35=119
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