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Question

Find the equation of a line passing through (1,2,3) having direction ratios 1,2,4

A
x11=y22=z33=r
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B
x12=y21=z43=r
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C
x11=y21=z43=r
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D
x11=y21=z34=r
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Solution

The correct option is D x11=y21=z34=r
We want to find the equation of a line and we are given the direction ratios and a point on the line. To find the line, let’s consider a general point P(x,y,z) on the same line.
Now the direction ratios of the line segment connecting P and Q should be proportional to 1,2,4
Direction ratio of line joining P and Q =x1,y2,z3
From question, direction ratios of the line = 1, 2, 4
Since these are proportional,
x11=y22=z34=r
Since any point on this line satisfies this condition, this is the equation of the line. This way of writing the equation of a line is called symmetrical form of a line.

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