find the direction cosines of the line x+2/2 = 2y-7/6 = 5-z/6 also find the vector equation of the line through the point A(-1,2,3) and parallel to the given line
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Step-by-step explanation:
Given line is
2
x+2
=
6
2y−7
=
6
5−z
→
2
x+2
=
3
y−7/2
=
−6
z−5
Direction ratios of the line are 2,3,−6
If a,b,c are the direction ratios of a line then direction cosines are
a
2
+b
2
+c
2
a
,
a
2
+b
2
+c
2
b
,
a
2
+b
2
+c
2
c
∴ direction cosines are
7
2
,
7
3
,
7
−6
And the line passing through (1,2,3) and parallel to the given line is
2
x−1
=
3
y−2
=
−6
z−3
The vector equation of the line can be written as :
r
=
i
^
+2
j
^
+3
k
^
+λ(2
i
^
+3
j
^
−6
k
^
), where λ is real.
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