Class 12 Maths - NCERT Chapter 11
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Relation: l² + m² + n² = 1
Proportional numbers to DC's
Finding DC's of the line connecting P(x1,y1,z1) and Q(x2,y2,z2)
Vector form: r = a + λb
Vector form: r = a + λ(b - a)
Using dot product of direction vectors
Non-parallel, non-intersecting lines
Using cross product formula
lx + my + nz = d
(r - a) . N = 0
Determinant form or (r-a).[(b-a)x(c-a)] = 0
x/a + y/b + z/c = 1
Family of planes: P1 + λP2 = 0
Condition for two lines to lie on same plane
Angle between their normal vectors
Perpendicular distance formula
Complement of angle between line and normal