Q4 of 76 Page 477

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector

We know that

Vector equation of a line that passes through a given point whose position vector is and parallel to a given vector is .


So, here the position vector of the point (1, 2, 3) is given by and the parallel vector is .


∴ The vector equation of the required line is:


, where is a real number.


More from this chapter

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2

Show that the line through the points (1, –1, 2), (3, 4, –2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

 3

Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (–1, –2, 1), (1, 2, 5).

 5

Find the equation of the line in vector and in cartesian form that passes through the point with position vector and is in the direction

6

Find the cartesian equation of the line which passes through the point (–2, 4, –5) and parallel to the line given by