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:
Now, first we rewrite the given equations according to the standard form, i.e.
and , i.e.
Now, comparing (i) and (ii), we get
Now, as both the lines are at right angles,
so a1a2 + b1b2 + c1c2 = 0
⇒ 11p = 70