Answer:
(a) 7x + 5y + 6z + 30 =
0
And 3x ? y ? 10z 4
= 0
On comparing given
planes with
A1x +
b1y + c1z + d1= 0
And a2x
+ b2y +| c2z + d2 =0
We get, a1
= 7, b1 = 5, c1 = 6
A2 = 3,
b2 = ?1, c2 = ?10
Let be the angle
between given planes.
(b) 2x+ y + 3z ? 2
= 0 and x ? 2y + 5 = 0
On
comparing given planes with a1x + b1y + c1z +
d1 = 0 and a2x + b2y + c2z + d2
= 0, we get a1 = 2, b1 = a, c1 = 3
a2
= 1, b2 = ?2, c2 = 0
As
a1a2+ b1 b2 + c1c2
= 2 × 1 + 1 × (?2) + 3
× 0 = 2 ? 2 + 0 =
0
given planes
are perpendicular to each other.
(a) 2x ? 2y + 4z + 5 = 0
and 3x ? 3y + 6z ? 1 =
0
On comparing given
planes with a1x + b1y + c1z + d1 =
0 and
a2x +
b2y + c2z + d2 = 0, we get,
a1 =
2, b1 = ?2, c1 = 4
a2 =
3, b2 = ?3, c2 = 6
Here
given planes
are parallel to each other.
(b) 2x ? y + 3z ? 1 = 0
and 2x ? y + 3z + 3 = 0
On comparing given
ploanes with a1 + b1y + c1z d1 = 0
a2x + b2y
+ c2z + d2 = 0, we get, a1 = 2, b1
= ?1, c1 = 3
a2 = 2,
b2 = ?1, c2 = 3
Clearly,
given planes
are parallel to each other.
(e) 4x + 8y + z ? 8 = 0
and y + z ? 4 = 0
On comparing given
planes with a1x + b1y + c1z + d1 =
0 and a2x + b2y + c2z + d2 = 0, we
get a1 = 4, b1 = 8, c1 = 1
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