Angle between a line and a plane :
The angle between a line and a plane is the complement of the angle between the line and the normal to
the plane
If `alpha, beta, gamma` be the direction ratios of the line and `ax + by + cz + d = 0` be the equation of plane and `theta` be the angle between the line and the
plane.
`=> cos (90^(circ) -theta) = (a alpha + b beta+c gamma)/(sqrt (a^2+b^2+c^2) sqrt (alpha^2+beta^2+gamma^2))`
or `sin theta = (a alpha + b beta+c gamma)/(sqrt (a^2+b^2+c^2) sqrt (alpha^2+beta^2+gamma^2))`
`text(Vector form :)`
If `theta` is the angle between the line; `vec(r)=vec(a)+lambdavec(b)` and plane `vec(r)*vec(n)=d`
`=> sin theta = (vec(b)*vec(n))/(|vec(b) | |vec(n) |)`
the plane
If `alpha, beta, gamma` be the direction ratios of the line and `ax + by + cz + d = 0` be the equation of plane and `theta` be the angle between the line and the
plane.
`=> cos (90^(circ) -theta) = (a alpha + b beta+c gamma)/(sqrt (a^2+b^2+c^2) sqrt (alpha^2+beta^2+gamma^2))`
or `sin theta = (a alpha + b beta+c gamma)/(sqrt (a^2+b^2+c^2) sqrt (alpha^2+beta^2+gamma^2))`
`text(Vector form :)`
If `theta` is the angle between the line; `vec(r)=vec(a)+lambdavec(b)` and plane `vec(r)*vec(n)=d`
`=> sin theta = (vec(b)*vec(n))/(|vec(b) | |vec(n) |)`