#### 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`

#### Solution

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.

Is there an error in this question or solution?

Solution 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 Concept: Plane - Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point.