MHT CET · Maths · Three Dimensional Geometry
The equation of the line passing through the point of intersection of \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\) and also through the point \((2,1,-2)\) is
- A \(\overline{\mathrm{r}}=(-\hat{i}-\hat{\mathrm{j}}-\hat{\mathrm{k}})+\lambda(\hat{i}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
- B \(\overline{\mathrm{r}}=(-\hat{i}-\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(2 \hat{i}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
- C \(\frac{x+1}{3}=\frac{y+1}{2}=\frac{z+1}{-1}\)
- D \(\frac{x-1}{3}=\frac{y-1}{2}=\frac{z+1}{1}\)
Answer & Solution
Correct Answer
(C) \(\frac{x+1}{3}=\frac{y+1}{2}=\frac{z+1}{-1}\)
Step-by-step Solution
Detailed explanation
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\lambda \Rightarrow x=2\lambda+1, y=3\lambda+2, z=4\lambda+3\) \(\frac{x-4}{5}=\frac{y-1}{2}=z=\mu \Rightarrow x=5\mu+4, y=2\mu+1, z=\mu\)
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