Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The given equation of the straight line is: $(x-3)/3=(y-2)/1=(z-1)/0$ The direction ratios of this line are 3,1, and 0. A line parallel to the $z$-axis has direction ratios 0,0, and 1. If the dot product of the direction ratios of two lines is zero, then the lines are perpendicular. Let's check the dot product of the direction ratios of the given line and a line parallel to the z-axis: $\left(3^{\ast }0\right)+(1\ast 0)+(0\ast 1)=0$ Since the dot product is zero, the given line is perpendicular to the z-axis. Therefore, the correct answer is (4).