Angle Between Two Lines

Question 1

Angle between lines L1 and L 2 terms of dc’s

Answer 1

cosθ=|l1l2 +m1m2 +n1n2|

Question 2

Angle between L1 and L2 in terms of dc’s in terms of sine

Answer 2

sinθ= sqrt(l1m2−l2m1)2−(m1n2−m2n1)2+(n1l2−n2l1)2

Question 3

Angle in terms of vector form given eqns r=a1+ñb1 r=a2+ub2

Answer 3

cosθ= |b1.b2|/||b1||b2||

Question 4

In cartesian form

Answer 4

cos θ = |a1a2+b1b2+c1c2|/|sqrt a1^2+b1^2+c1^2 * sqrt a2^2+b2^2+c2^2 * sqrt a3^2+b3^2+c3^2|

Question 5

Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are (i) perpendicular i.e. if θ = 90° (ii) parallel i.e. if θ = 0

Answer 5

1: a1a2 +b1b2 +c1c2 =0
2: a1/a2=b1/b2=c1/c2