- Equation of a line through a given point and parallel to a given vector
- Equation of a line passing through two given points
- Vector and Cartesian Equation of a Line
- Find the Equation of a Line Given Two Points
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- Three Dimensional Geometry Part 2 -Straight Line
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- 3 Dimensional Geometry part 8 (Equation of line through 2 point)
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- 3 Dimensional Geometry part 9 (Example:- Line through 2 points)
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- 3 Dimensional Geometry part 7 (Example:- Equation of Line)
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- 3 Dimensional Geometry part 5 (Equation of Line:- Vector)
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- 3 Dimensional Geometry part 6 (Equation of Line:- Cartesian)
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Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).
Find the vector and Cartesian equations of a line passing through (1, 2, –4) and perpendicular to the two lines `(x - 8)/3 = (y + 19)/(-16) = (z - 10)/7` and `(x - 15)/3 = (y - 29)/8 = (z - 5)/(-5)`
Find the vector and Cartesian equations of the line through the point (1, 2, −4) and perpendicular to the two lines.
`vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) " and "vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)`
Find the Cartesian equation of the line which passes through the point (−2, 4, −5) and is parallel to the line `(x+3)/3=(4-y)/5=(z+8)/6`
Find the vector and cartesian equations of the line passing through the point (2, 1, 3) and perpendicular to the lines
`(x-1)/1=(y-2)/2=(z-3)/3 and x/(-3)=y/2=z/5`
Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).
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).
If the Cartesian equations of a line are ` (3-x)/5=(y+4)/7=(2z-6)/4` , write the vector equation for the line.
Find the vector and the Cartesian equations of the lines that pass through the origin and (5, −2, 3).
Find the equation of the line in vector and in Cartesian form that passes through the point with position vector `2hati -hatj+4hatk` and is in the direction `hati + 2hatj - hatk`.
A line passes through (2, −1, 3) and is perpendicular to the lines `vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk)` . Obtain its equation in vector and Cartesian from.
Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.
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).
Show that the lines `(x-5)/7 = (y + 2)/(-5) = z/1` and `x/1 = y/2 = z/3` are perpendicular to each other.
Show that the three lines with direction cosines `12/13,(-3)/13,(-4)/13; 4/13,12/13,3/13;3/13,(-4)/13,12/13 ` are mutually perpendicular.
Find the value of p, so that the lines `l_1:(1-x)/3=(7y-14)/p=(z-3)/2 and l_2=(7-7x)/3p=(y-5)/1=(6-z)/5 ` are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, – 4) and parallel to line l1.
The Cartesian equation of a line is `(x-5)/3 = (y+4)/7 = ("z"-6)/2` Write its vector form.
The given line passes through the point (5, −4, 6). The position vector of this point is `veca = 5hati - 4hatj + 6hatk`
Also, the direction ratios of the given line are 3, 7, and 2.
This means that the line is in the direction of vector, `vecb =3hati +7hatj + 2hatk`
It is known that the line through position vector `veca` and in the direction of the vector `vecb`is given by the equation, `vecr = veca+lambdavecb, lambda in R`
This is the required equation of the given line in vector form.
Find the Cartesian equation of the line which passes through the point (−2, 4, −5) and parallel to the line given by `(x+3)/3 = (y-4)/5 = ("z"+8)/6`