Find the equation of a line passing through (1,2,3) having direction ratios 1,2,4
A
x−11=y−22=z−33=r
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B
x−12=y−21=z−43=r
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C
x−11=y−21=z−43=r
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D
x−11=y−21=z−34=r
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Solution
The correct option is Dx−11=y−21=z−34=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 =x−1,y−2,z−3 From question, direction ratios of the line = 1, 2, 4 Since these are proportional, x−11=y−22=z−34=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.