# Find the ve

Vector equation of the line passing through and is Where, and Therefore, vector equation of required line is  Now, equation of z-axis is As Therefore, the line is perpendicular to z-axis.

We can also do the last step as follows,

We know that if a1, b1, c1 are direction Ratios of a line perpendicular to line with direction Ratios a2, b2, c2 then,

a1a2 + b1b2 + c1c2 = 0

Equation of line: If equation of line is, Then, is a point through the line passes, and <a, b, c> is its direction ratio.

Direction Ratio of z-axis is <0, 0, 1>

Direction Ratio of line <-4, 2, 0>

a1a2 + b1b2 + c1c2 = (0)(-4) + (0)(2) + (1)(0)

= 0 + 0 + 0

= 0

So, the line is perpendicular to z – axis.

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