Question

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes `vecr = (hati - hatj + 2hatk)  = 5`and `vecr.(3hati + hatj + hatk) = 6`

Answer 1

Let the required line be parallel to vector `vecb` given by,

`vecb = b_1hati + b_2hatj + b_3hatk`

The position vector of the point (1, 2, 3) is `veca = hati + 2hatj + 3hatk`

The equation of line passing through (1, 2, 3) and parallel to `vecb`is given by,

This is the equation of the required line.