Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector .
It is given that the line passes through the point ( 1 , 2 , 3 ) and is parallel to the vector 3 i ^ + 2 j ^ − 2 k ^ .
The equation of a line passing through a point ( 1 , 2 , 3 ) with position vector m → and parallel to a vector n → is,
r → = m → + λ n → (1)
The given line passing through ( 1 , 2 , 3 ) has position vector as,
m → = 1 i ^ + 2 j ^ + 3 k ^
As the given line is parallel to vector 3 i ^ + 2 j ^ − 2 k ^ , then
n → = 3 i ^ + 2 j ^ − 2 k ^
Substitute the values of m and n in equation (1).
r → = ( 1 i ^ + 2 j ^ + 3 k ^ ) + λ ( 3 i ^ + 2 j ^ − 2 k ^ )
Thus, the equation of the line is r → = ( 1 i ^ + 2 j ^ + 3 k ^ ) + λ ( 3 i ^ + 2 j ^ − 2 k ^ ) .
It is given that the line passes through the point
The equation of a line passing through a point
The given line passing through
As the given line is parallel to vector
Substitute the values of m and n in equation (1).
Thus, the equation of the line is
