99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

If the d.r.'s of two lines are connected by the relations a - b + c =0, a ^2- b ^2+2 c ^2=0 and is the angle between these lines then =

Options

A2 7
B3 2 7
C3 4 2
D1 3 2

Correct answer

A. 2 7

Step-by-step solution

We have relations between two lines as a-b + c =0 and a ^2- b ^2+2 c ^2=0 from (i) c=b-a put value of c in equation (ii) aligned & a ^2- b ^2+2( ~b - a )^2=0 & (3 a - b )( a - b )=0 & a : b =1: 3 or a : b =1: 1 aligned Thus a: b : c =1: 3: 2 or a : b : c =1: 1: 0 now angle between lines is = (1,3,2)(1,1,0) 1^2+3^2+2^2 1^2+1^2 = 2 7

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