Question

The value of${}^{\prime }{a}^{\prime }$ for which the lines $\frac{x-2}{1}=\frac{y-9}{2}=\frac{z-13}{3}and\frac{x-a}{-1}=\frac{y-7}{2}=\frac{z+2}{-3}intersectis$

• A. $-5$
• B. $-2$
• C. $5$
• D. $-3$

Answer 1

The correct option is A $-5$

We have,

Condition on lines

$\frac{x-2}{1}=\frac{y-9}{2}=\frac{z-13}{3}......\left(1\right)$

$\frac{x-\alpha }{-1}=\frac{y-7}{2}=\frac{z+2}{-3}......\left(2\right)$

To intersects is,

So, for the given lines to intersects, we

must have,

$\Rightarrow (a-2)[-6-6]+2[-3+3]+15[2+2]=0$

$\Rightarrow -12(a-2)+60=0$

$\Rightarrow -12(a-2)=-60$

$\Rightarrow a-2=5$

$\Rightarrow a=5+2$

$\Rightarrow a=7$

Hence, this is the answer.