Question

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{5t-1}$ and $\frac{x+1}{2s+1}=\frac{y}{2}=\frac{z}{4}$ are parallel to each other, then value of s,t will be

• A. $6,\frac{5}{7}$
• B. $\frac{1}{2},1$
• C. $3,\frac{5}{7}$
• D. $4,\frac{7}{10}$

Answer 1

The correct option is B $\frac{1}{2},1$

$L_1:\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{5t-1}$

$L_2:\frac{x+1}{2s+1}=\frac{y}{2}=\frac{z}{4}$

Since $L_1\parallel L_2$ $\therefore$ their slopes are equal

$\therefore a_1=a_2,b_1=b_2$ and $c_1=c_2$

$2=2s+1$

$2s=1$

$s=\frac{1}{2}$

$5t-1=4$

$5t=5$

$t=1$

$\therefore s,t=1$