Passes through (1,-2) parallel to line containing points (-2,1) and (1,5)
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Class 12
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>>Three Dimensional Geometry
>>Equation of a Line in Geometry
>>Find the vector equation of...
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Find the vector equation of the line passing through the point A(1,2,−1) and parallel to the line 5x−25=14−7y=35z.
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Solution
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Given line is
5x−25=14−7y=35z
⇒
1/5
x−5
=
1/7
2−y
=
1/35
z−0
⇒
1/5
x−5
=
−1/7
y−2
=
1/35
z−0
=
7
x−5
=
−5
y−2
=
1
z−0
...(i)
Hence, parallel vector of given line i.e.,
b
=7
i
^
−5
j
^
+
k
^
Since required line is parallel to given line (i)
⇒
b
=7
i
^
−5
j
^
+
k
^
will also be parallel vector of required line which passes through A(1,2,−1).
Therefore, required vector equation of line is
r
=(
i
^
+2
j
^
−
k
^
)+λ(7
i
^
−5
j
^
+
k
^
)