51.Find a vector equation of the line through the points A (3, 4, – 7) and B (1, – 1, 6).
The line passes through the points A (3, 4, – 7), B (1, – 1, 6) where  are position vectors of A and B respectively.    Let  be the position vector of any point on the given line. ∴   the vector equation of the line is or    where λ is a parameter.
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52.Find the vector equation for the line passing through the points (– 1, 0, 2) and (3, 4, 6).
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53.Find the vector and cartesian equations of the line that passes through the origin and (5,- 2, 3).
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54.Find the vector and the cartesian equations of the line that passes through the points (3, – 2, – 5), (3, – 2, 6).
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55.Find the vector equation of line joining the points whose vectors areÂ
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56.If the points (–1, 3, 2), (– 4, 2, –2) and (5, 5, λ) are collinear, then find the value of λ.
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Long Answer Type
57.Show that the points whose position vectors are given by  are collinear.Â
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Short Answer Type
58.
Show that the point whose position vectors are given by  are collinear.Â
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Long Answer Type
59.Find the coordinates of the point where the line through A(3, 4, 1) and B (5, 1, 6) crosses the x y-plane.
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60.Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the YZ-plane.
Short Answer Type
 are position vectors of A and B respectively.
   
 be the position vector of any point on the given line. 
 where λ is a parameter.
Long Answer Type
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 are collinear. 
 are collinear. 
