Q. 74.5( 23 Votes )
The Cartesian equation of a line is 
. Write its vector form.
Answer :
We know that
The Cartesian equation of a line through a point (x1, y1, z1) and having direction cosines l, m, n is 
.
Comparing this standard form with the given equation, we get
x1 = 5, y1 = -4, z1 = 6 and l = 3, m = 7, n = 2
⇒ The point through which the line passes has the position vector 
and the vector parallel to the line is given by 
.
Now, ∵ Vector equation of a line that passes through a given point whose position vector is 
and parallel to a given vector 
is 
.
∴ The vector equation of the required line is:
⇒ 
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and 
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