Find the values of p so that the lines are at right angles.

For any two lines to be at right angles, the angle between them should be θ = 90°.

⇒ a₁a₂ + b₁b₂ + c₁c₂ = 0, where a₁, b₁, c₁ and a₂, b₂, c₂ are the direction ratios of two lines.

The standard form of a pair of Cartesian lines is:

and …(i)

Now, first we rewrite the given equations according to the standard form, i.e.

and , i.e.

and …(ii)

Now, comparing (i) and (ii), we get

and

Now, as both the lines are at right angles,

so a₁a₂ + b₁b₂ + c₁c₂ = 0

⇒

⇒

⇒

⇒

⇒ 11p = 70

⇒