Question

If a line passing through (2.1.-4) cuts off an intercept of minimum length between two non coplanar lines x-6-z and x =y=z, then α is equal to A) -2 B) 0 C) 1 D) 2 pls ans fast

Answer 1

Given:

A line passing through points (2,1,-4)

And two non - coplaner lines x-6-z and x=y=z

To Find:

 Value of α ?

Step-by-step explanation:

• we have provided two non - coplanar  lines

  $\bf x-6=\frac{y}{\alpha }=-z, x=y=z$

• For the intercept of minimum length  line passing through (2,1,4)

       should be perpendicular to lines

          $\bf x-6=\frac{y}{\alpha}=-z$

• Thus we can write

       $\bf -1(1)+ 1\times\alpha+(-1)1=0\\\\-2+\alpha=0\\\\\alpha=2$

Hence, value of α is 2