Book: Mathematics Part-II
Chapter: 11. Three Dimensional Geometry
Subject: Maths - Class 12th
Q. No. 12 of Exercise 11.2
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12
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
⇒ 
12
