53.Find the vector and cartesian equations of the line that passes through the origin and (5,- 2, 3).
The line passes through the points A(0, 0, 0) and B(5, – 2, 3) where are position vectors of A, B respectively. Let be the position vector of any point on the given line. ∴ the vector equation of line is or or Taking the equation of line is Comparing the coefficients of or which is cartesian equation of line.
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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 are
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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.
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Short Answer Type
58.
Show that the point whose position vectors are given by are collinear.
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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, B respectively.
be the position vector of any point on the given line.
the equation of line is
Long Answer Type
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are collinear. 
are collinear. 
