The planes: 2x – y + 4z = 5 and 5x – 2 5y + 10z = 6 are
(A) Perpendicular
(B) Parallel
(C) intersect y-axis
(D) passes through 
5
0,0,
4






Summary
� Direction cosines of a line are the cosines of the angles made by the line
with the positive directions of the coordinate axes � If l, m, n are the direction cosines of a line, then l2 + m 2 + n2 = 1 � Direction cosines of a line joining two points P(x1, y1, z1) and Q(x2, y2, z2) are
2
1
2
1
2
1
,
,
PQ
PQ
PQ
x
x
y
y
z
z
−
−
−
where PQ =   
(
)
12
2
2
1
2
2
1
2
)
(
)
(
z
z
y
y
x
x
−
+
−
+
−
� Direction ratios of a line are the numbers which are proportional to the
direction cosines of a line