Equation of line passing through the points (a,2−4) and (5,3,b) is given by
x−a
5−a
=
y−2
3−2
=
z+4
b+4
⇒
x−a
5−a
=
y−2
1
=
z+4
b+4
. . . (i) The equation of ZX -plane, y=0 Since, line (i) meetsthe ZX -plane. ⇒
x−a
5−a
=
0−2
1
=
z+4
b+4
⇒
x−a
5−a
=−2 and
z+4
b+4
=−2 ⇒x−a=−2(5−a) and z+4=−2(b+4) ⇒x=a−10+2a and z+4=−2b−8 ⇒x=3a−10 and z=−2b−12 and y=0 ∴3a−10=−a+2b and −2b−12=a+b ⇒4a−2b=10 and a+3b=−12 . . . (ii) ⇒2a−b=5 . . . (iii) On solving Eqs (i) and (ii), we get a=