Question

derive the equation of a line in space passing through 2 given points both in vector and cartesian form​

Answer 1

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Answer 2

$\bf\large\underline\blue{Answer:-}$

A line is determined by a point and a direction. Thus, to find an equation representing a line in three dimensions choose a point P

0

on the line and a non-zero vector

′

v

′

parallel to the line.

Since any constant multiple of a vector still points in the same direction, it seems reasonable that a point on the line can be found by starting at the point P

0

on the line and following a constant multiple of the vector v (see the figure above).

If

′

r

′

is the position vector of P, then the line must be in the form

r

=

r

0

+t

v

Let the direction ratios of the line be a,b,c. Consider coordinates of any point A be (x,y,z).

Then Cartesian form of a line is given by

a

x−x

0

=

b

y−y

0

=

c

z−z

0