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Byju's Answer
Standard XII
Mathematics
Point Slope Form of a Line
Write the dir...
Question
Write the direction cosines of the line whose cartesian equations are 6x − 2 = 3y + 1 = 2z − 4.
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Solution
We have
6x − 2 = 3y + 1 = 2z − 4
The equation of given line can be re-written as
x
-
1
3
1
6
=
y
+
1
3
1
3
=
z
-
2
1
2
⇒
x
-
1
3
1
=
y
+
1
3
2
=
z
-
2
3
The direction ratios of the line parallel to AB are proportional to 1, 2, 3.
Hence, the direction cosines of the line parallel to AB are proportional to
1
1
2
+
2
2
+
3
2
,
2
1
2
+
2
2
+
3
2
,
3
1
2
+
2
2
+
3
2
=
1
14
,
2
14
,
3
14
.
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