3D Geometry Notes
3D Geometry Notes
3D Geometry Notes
https://t.me/vedantumath1/3938
3. Equation of a Line
2. Direction Ratios of a Line (DR’s)
1. Equation of a line through a given point with
Any three numbers a, b and c proportional to the position vector and parallel to a given vector :
direction cosines l, m and n, respectively are called In vector form,
direction ratios of the line. In cartesian form,
● The direction ratios of a line passing through
two points P(x1, y1, z1) and Q(x2, y2, z2) are
(x2 - x1), (y2 - y1), (z2 - z1) where,
Here, a, b, c are also the direction ratios of the line
● 2. Equation of a line passing through two given
points with position vectors
● In vector form,
In cartesian form,
4. Angle between Two Lines 3D - Geometry 5. Shortest Distance between Two Lines
In vector form, 1. Distance between Parallel Lines
The angle between two lines The shortest distance parallel lines
In cartesian form,
The distance between two skew lines
Type 1
Shortest distance between two lines
A 8
B 7
C 6
D 9
A 8
B 7
C 6
D 9
Solution
Solution
If the shortest distance between the lines
Type 2
Intersection of two lines and angle
between them
Correct answer is 18
Solution
Solution
Solution
A 9
B √74
C √69
D √54
A 9
B √74
C √69
D √54
Solution
Solution
Types of Problems
Type 3
Image of Point & Foot of
Perpendicular from point
A
D
A
D
Solution
Solution
Correct answer is 4
Solution
3D - Geometry
https://t.me/vedantumath1/3938