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- 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
- 3 Dimensional Geometry part 9 (Example:- Line through 2 points)
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- 3 Dimensional Geometry part 8 (Equation of line through 2 point)
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- Find the Equation of a Line Given Two 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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- Three Dimensional Geometry Part 2 -Straight Line
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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 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.
Let `A(bara)` and `B(barb)` be any two points in the space and `R(barr)` be a point on the line segment AB dividing it internally in the ratio m : n, then prove that `bar r=(mbarb+nbara)/(m+n)` . Hence find the position vector of R which divides the line segment joining the points A(1, –2, 1) and B(1, 4, –2) internally in the ratio 2 : 1.
If a line drawn from the point A( 1, 2, 1) is perpendicular to the line joining P(1, 4, 6) and Q(5, 4, 4) then find the co-ordinates of the foot of the perpendicular.
The joint equation of the pair of lines passing through (2,3) and parallel to the coordinate axes is
- xy -3x - 2y + 6 = 0
- xy +3x + 2y + 6 = 0
- xy = 0
- xy - 3x - 2y - 6 = 0
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 ``
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`
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 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.