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Previous Year Question (PYQs)



Let the equation of a straight line passing through point $A(\alpha,\beta,\gamma)$ and having direction ratios $l,m,n$ be $\dfrac{x-\alpha}{l}=\dfrac{y-\beta}{m}=\dfrac{z-\gamma}{n}=r$ Suppose $P$ is any arbitrary point on this line with coordinates $(\alpha+lr,\beta+mr,\gamma+nr)$. Geometrically, $r$ is





Solution

Distance $AP = \sqrt{(lr)^2+(mr)^2+(nr)^2}$ $= |r|\sqrt{l^2+m^2+n^2}$ So distance is proportional to $r$.


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