MHT CET · Maths · Vector Algebra
If a point \(\mathrm{P}\) on the line segment joining the points \((3,5,-1)\) and \((6,3,-2)\) has
its y - coordinate 2, then its z - coordinate is
- A \(\frac{2}{15}\)
- B \(\frac{17}{3}\)
- C \(\frac{15}{2}\)
- D \(\frac{3}{17}\)
Answer & Solution
Correct Answer
(C) \(\frac{15}{2}\)
Step-by-step Solution
Detailed explanation
Equation of line passing through \((3,5,-1)\) and \((6,3,-2)\) is
\(
\frac{x-3}{3}=\frac{y-5}{-2}=\frac{z+1}{-1}=r(\text { say })
\)
Hence coordinates of any point lying on the line are \((3 r+3,-2 r+5,-r-1)\)
We have \(-2 r+5=2 \Rightarrow \quad r=\frac{3}{2}\)
\(\therefore z\) coordinate is \(-r-1=\frac{-3}{2}-1=\frac{-5}{2}\)
\(
\frac{x-3}{3}=\frac{y-5}{-2}=\frac{z+1}{-1}=r(\text { say })
\)
Hence coordinates of any point lying on the line are \((3 r+3,-2 r+5,-r-1)\)
We have \(-2 r+5=2 \Rightarrow \quad r=\frac{3}{2}\)
\(\therefore z\) coordinate is \(-r-1=\frac{-3}{2}-1=\frac{-5}{2}\)
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