Q. 205.0( 1 Vote )

# Find the value of

Formula: -

(i)in Cartesian form of the lines

And

(ii) Two line with direction ratio and are perpendicular if then

Given: -

And

Arranging the above

and

Arranging the above equation as in form of

And

So, the Cartesian form is

Where x1 = 5, x2 = 0, y1 = 2, y2 = - �, z1 = 1,z2 = 1,

a1 = 5λ+2, a2 = 1, b1 = -5, b2 = 2λ,c1 = 1,c2 = 3

The direction ratio of these lines are and5λ+2, -5,1 and 1, 2λ ,3

Since the line are perpendicular

Then using formula (ii)

a1a2 + b1b2 +c1c2 = 0

(5λ+2)(1)+(-5)(2λ)+1(3) = 0

5λ+2-10λ+3 = 0

-5λ = -5

λ = 1

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