Question

The direction ratios of a line \(L\) are \((ab,b,b)\) \((b\gt 0)\) and the line \(L\) passes through \[ P(b,b,b). \] If \(Q(x,y,z)\) is a point on the line at a distance of \(b\) units from \(P\), then \[ x+y+z= \]

• A. \[ b\left(3\pm\frac{a+2}{\sqrt{a^2+2}}\right) \]
• B. \[ b\left(3\pm\frac{a^2-2}{\sqrt{a^2+2}}\right) \]
• C. \[ b\left(a\pm\frac{a+2}{\sqrt{a^2+2}}\right) \]
• D. \[ b\left(a\pm\frac{a^2-2}{\sqrt{a^2+2}}\right) \]

Hint:

To find a point at a given distance along a line, first convert the direction ratios into a unit vector. Then use \[ \text{New Point} = \text{Given Point} \pm (\text{Distance})\times(\text{Unit Vector}). \]

Answer 1

The Correct Option is A