Answer :

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 a_{1}, b_{1}, c_{1} are direction Ratios of a line perpendicular to line with direction Ratios a_{2}, b_{2}, c_{2} then,

a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 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>

a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = (0)(-4) + (0)(2) + (1)(0)

= 0 + 0 + 0

= 0

So, the line is perpendicular to z – axis.

Rate this question :

Find the equationMathematics - Board Papers

Find the vector aMathematics - Board Papers

Write the vector Mathematics - Board Papers

Find the value ofMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers