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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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


Now, as both the lines are at right angles,

so a1a2 + b1b2 + c1c2 = 0

11p = 70


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