Pls explain the answers of all the questions
Pls answer by this night as i have my exams tomorrow morning by 7 am
Topic : Vectors

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \frac{\mathrm{x}-3}{1}=\frac{\mathrm{y}+3}{5}=\frac{2\mathrm{z}-5}{3} \\ \Rightarrow \frac{\mathrm{x}-3}{1}=\frac{\mathrm{y}+3}{5}=\frac{\mathrm{z}-5}{{\displaystyle \frac{3}{2}}} \\ \mathrm{Any} \mathrm{line} \mathrm{parallel} \mathrm{to} \mathrm{above} \mathrm{line} \mathrm{will} \mathrm{have} \mathrm{same} \mathrm{direction} \mathrm{ratios} \mathrm{and} \mathrm{hence} \\ \mathrm{will} \mathrm{have} \mathrm{equation} \mathrm{as} \\ \frac{\mathrm{x}-{\mathrm{x}}_1}{1}=\frac{\mathrm{y}-{\mathrm{y}}_1}{5}=\frac{\mathrm{z}-{\mathrm{z}}_1}{{\displaystyle \frac{3}{2}}}=\mathrm{t} \\ \mathrm{As} \mathrm{line} \mathrm{passes} \mathrm{through} \left(1,3,5\right), \mathrm{hence} \left({\mathrm{x}}_1,{\mathrm{y}}_1,{\mathrm{z}}_1\right)=\left(1,3,5\right) \\ \Rightarrow \frac{\mathrm{x}-1}{1}=\frac{\mathrm{y}-3}{5}=\frac{\mathrm{z}-5}{{\displaystyle \frac{3}{2}}}=\mathrm{t} \\ \Rightarrow \left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(1+\mathrm{t},3+5\mathrm{t},5+\frac{3\mathrm{t}}{2}\right) \\ \mathrm{Hence} \mathrm{option} \left(4\right) \mathrm{is} \mathrm{correct}. \end{gathered}$$

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