Mathematics Part-II

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



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