Q23 of 29 Page 1

Find the vector equation of the line joining (1, 2, 3) and (-3, 4, 3) and show that it is perpendicular to the z-axis.

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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