Question:
The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is
The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is
Options:
- (0, 0, 3)
- (-1, 1, 3)
- (0, 1, 2)
- (1, 1, 1)
- (0, 0, 3)
- (-1, 1, 3)
- (0, 1, 2)
- (1, 1, 1)
Correct Answer: d)
Explanation:
‘ The f∞t (x,y, z) of a point (z1,y1, 21) in a plane az + by + cz + d = 0 is gi√en by ‘
1 zor YH za 1
h a b 3 H
_ (az +by; tea +d)
‘ TTT ate
1 .”. The f∞t (x,y, 2) of a point
‘ (0,0,0) in a plane + y+ z — 3 = 0 is gi√en by
x20 _ y= 0 _ 2-1
\ T — 1 ~ 1 \
H _ —(1×0+1×0+1×0-3) H
_y_z_3
! =f=1=1=3%
1 >3=i=%=1
‘ sz=1Ly=1z2=1
Hence, required f∞t of the perpendicular is (1,1,1).
Ln
‘ (d) None of these
‘ The f∞t (x,y, z) of a point (z1,y1, 21) in a plane az + by + cz + d = 0 is gi√en by ‘
1 zor YH za 1
h a b 3 H
_ (az +by; tea +d)
‘ TTT ate
1 .”. The f∞t (x,y, 2) of a point
‘ (0,0,0) in a plane + y+ z — 3 = 0 is gi√en by
x20 _ y= 0 _ 2-1
\ T — 1 ~ 1 \
H _ —(1×0+1×0+1×0-3) H
_y_z_3
! =f=1=1=3%
1 >3=i=%=1
‘ sz=1Ly=1z2=1
Hence, required f∞t of the perpendicular is (1,1,1).
Ln
‘ (d) None of these