Lines in Space
• Equation of lines in space can be uniquely determined in the following two conditions:
a) If the line in space passes through a given point and parallel to a given line.
b) If the line in space passes through two given points.
• In three dimensional geometry the equations of xaxis are y = 0, z = 0; the equations of yaxis are x = 0, z = 0 and the equations of zaxis are y = 0, x = 0.
• Equation of a line in space passing through a given point and parallel to a given vector can be expressed in two forms viz. vector form and Cartesian form.
• The Cartesian form of a line in space passing through a given point (x1, y1, z1) and parallel to a given vector with direction ratios a, b and c is as follows:
(x – x1)/a = (y – y1)/b = (z – z1)/c
• Equation of a line passing through two given points (x1, y1, z1) and (x2, y2, z2) in the Cartesian form is as follows:
(x – x1)/ (x2 – x1) = (y – y1)/ (y2 – y1) = (z – z1)/ (z2 – z1)
Keywords: Equation of a line in space, Equation of a line through a given point and parallel to a given vector, Equation of a line through two given points, Angle between two lines
To Access the full content, Please Purchase

Q1Marks:1
Answer:

Q2Marks:1
Answer:

Q3Marks:1
Answer:

Q4Marks:2
Answer:

Q5
Find the vector equation of the line through points A (1, 4, –5) and B (1, –1, 7).
Marks:1Answer: