Question:
Under what condition do the planes bx – ay = n, cy – bz = l and az – cx = m intersect in a line?
Under what condition do the planes bx – ay = n, cy – bz = l and az – cx = m intersect in a line?
Options:
- l + m + n = 0
- a = b = c
- a + b + c = 0
- al + bm + cn = 0
- l + m + n = 0
- a = b = c
- a + b + c = 0
- al + bm + cn = 0
Correct Answer: d)
Explanation:
!
1 y
A
00.2 yo)
SEAN
1 al A 2.0.0) 1
5020) 78
Y
i The gi√en planes are
1 bx-ay-n=0..(i)
‘ cy -bz-1=0..(ii)
i az-cx -m=0..(iii)
1 The equation of planes passing through the line of ∩ion of planes (i) and (ii) are
‘ (bz —ay—n)+ A(cy—bz—1)=0
‘ or bz + (—a + Ac)y — (bA)z-+(—n — Al) = 0 …(i√) ‘
1 Egs. (iii) and (i√) are identical.
Lb _ —atde _ —bX
1 √e 0 7 Ta 1
1 _ (nt) 1
– —m
= A=Zand = mn
La _ —bm-cn
1 eT Ta !
i =al+bm+cn=0
170.
®) (3,2,1) 1
i
!
1 y
A
00.2 yo)
SEAN
1 al A 2.0.0) 1
5020) 78
Y
i The gi√en planes are
1 bx-ay-n=0..(i)
‘ cy -bz-1=0..(ii)
i az-cx -m=0..(iii)
1 The equation of planes passing through the line of ∩ion of planes (i) and (ii) are
‘ (bz —ay—n)+ A(cy—bz—1)=0
‘ or bz + (—a + Ac)y — (bA)z-+(—n — Al) = 0 …(i√) ‘
1 Egs. (iii) and (i√) are identical.
Lb _ —atde _ —bX
1 √e 0 7 Ta 1
1 _ (nt) 1
– —m
= A=Zand = mn
La _ —bm-cn
1 eT Ta !
i =al+bm+cn=0
170.
®) (3,2,1) 1
i