Question

Find the vector equation of a line joining 1 2 3 and minus 3 4 3 show that it is perpendicular to the Z axis

Answer 1

Answer:

Step-by-step explanation:

we know, vector equation of a line passing through two points  and is given by,

here, two points are :  and

so,

and

so,

hence, equation of line is

also we can prove that, line  is perpendicular to the z axis by using dot product.

unit vector along z - axis is

so, direction ratio of z - axis (0, 0, 1)

and direction ratio of line : (-4, 2, 0)

we know, if two lines of direction ratios  and  are perpendicular to each other then,

here, 0 × -4 + 0 × 2 + 1 × 0 = 0

hence, line is perpendicular to the z - axis.