Find the direction ratio of a line perpendicular to both the lines whoes direction equation are 3,2,-1 and 2,4-2
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Answer:
Step-by-step explanation:
Given direction ratios are :−2,1,−1 and −3,−4,1
Let a,b and c be the direction ratios of the line perpendicular to the given lines.
Thus, we have,
−2a+b−c=0
−3a−4b+c=0
Cross multiplying, we get
1×1−(−4)×(−1)
a
=
(−3)×(−1)−(−2)×1
b
=
−2×−4−(−3)×1
c
⇒
1−4
a
=
3+2
b
=
8+3
c
⇒
−3
a
=
5
b
=
11
c
Let us find
a
2
+b
2
+c
2
=
(−3)
2
+5
2
+11
2
=
9+25+121
=
155
Thus, the direction ratios of the required line are −3,5,11
The direction cosines are :
155
−3
,
155
5
,
155
11
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