Q. 16 C5.0( 2 Votes )

# Find the angle be

Answer :

Given relations are:

3lm–4ln+mn=0 ……(1)

l+2m+3n=0

l=–2m–3n ……(2)

Substituting (2) in (1) we get,

3(–2m–3n)m –4(–2m–3n)n +mn =0

3(–2m2–3mn) –4(–2mn–3n2) +mn=0

–6m2–9mn+8mn+12n2+mn=0

12n2–6m2=0

m2–2n2=0   ……(3)

Substituting the values of (3) in (2) we get,

For the 1st line:  The Direction Ratios for the 1st line is .

For the 2nd line:  The Direction Ratios for the 2nd line is .

We know that the angle between the lines with direction ratios proportional to (a1,b1,c1) and (a2,b2,c2) is given by: Using the above formula we calculate the angle between the lines.

Let be the angle between the two lines given in the problem.     The angle between two lines is .

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