Name______________________________________
Equations of Lines
Find a vector equation of each line described.
1 
1) passing through (3, -4) and in the direction   .
 4
2) passing through (–1, 4) and (3, –1)
3) passing through (0, 1, -1) and (5, -1, 3)
 2
4) Find the parametric equations of the line passing through (-1, 4) with direction vector   and parameter s.
 1 
Find points on the line when s = 0, 1, 3, -1, -4.
5) Does (3, -2) lie on the line with parametric equations x = t + 2,y = 1 – 3t ? Does (0, 6) lie on this line?
6) The vector equations of two lines are given below. The lines intersect at the point P. Find the position
 5
 3 
 – 2
 4
vector of P. r1 =   + s   , r2 =   + t  
 – 2
 2 
 1
 1
7) (k, 4) lies on the line with parametric equations x  1  2t , y  1  t . Find k.
8) Find a vector equation for the line passing through the point (4, 3) and parallel to the vector i – 2j.
 x   1  2 
 x  1   1 
     
     
9) Line 1 has equation:  y    1   s  2  and line 2 has equation  y    0   t  1  . Determine whether
z   1   4 
 z   3   2 
     
     
the lines are parallel, perpendicular or neither. Justify your answer.
10) Line 3 has equations x  1  2 s, y  1  2 s and z  1  4 s .
Line 4 has equations x  1  t , y  t and z  3  2t .
Line 5 has equations x  1  2u, y  1  u and z  4  3u.
a) Show that line 3 and line 4 intersect and find the angle between them.
b) Show that line 3 and line 5 are skew (not intersecting or parallel)
Name______________________________________
Equations of Lines
Find a vector equation of each line described.
1 
1) passing through (3, -4) and in the direction   .
 4
2) passing through (–1, 4) and (3, –1)
3) passing through (0, 1, -1) and (5, -1, 3)
 2
4) Find the parametric equations of the line passing through (-1, 4) with direction vector   and parameter s.
 1 
Find points on the line when s = 0, 1, 3, -1, -4.
5) Does (3, -2) lie on the line with parametric equations x = t + 2,y = 1 – 3t ? Does (0, 6) lie on this line?
6) The vector equations of two lines are given below. The lines intersect at the point P. Find the position
 5
 3 
 – 2
 4
vector of P. r1 =   + s   , r2 =   + t  
 – 2
 2 
 1
 1
7) (k, 4) lies on the line with parametric equations x  1  2t , y  1  t . Find k.
8) Find a vector equation for the line passing through the point (4, 3) and parallel to the vector i – 2j.
 x   1  2 
 x  1   1 
     
     
9) Line 1 has equation:  y    1   s  2  and line 2 has equation  y    0   t  1  . Determine whether
z   1   4 
 z   3   2 
     
     
the lines are parallel, perpendicular or neither. Justify your answer.
10) Line 3 has equations x  1  2 s, y  1  2 s and z  1  4 s .
Line 4 has equations x  1  t , y  t and z  3  2t .
Line 5 has equations x  1  2u, y  1  u and z  4  3u.
a) Show that line 3 and line 4 intersect and find the angle between them.
b) Show that line 3 and line 5 are skew (not intersecting or parallel)