Core Pure Vectors by James RUDGE

Equation of a Plane

19krishnag — 2018-04-16 05:00:58 UTC

(1) Cartesian Form:
ax + by + cz = d
- Note that (a, b, c) is the normal vector
- Therefore, r.(a,b,c) = d can be easily converted into Cartesian form.
(2) Vector equation of a plane
r = (x,y,z) + N(d,e,f) + M(g,h,i)
- Think of this as a point and multiples of two non-parallel lines - this can get to any position on a 2D plane in 3D space.

Bryan

2018-04-16 05:01:34 UTC

scalar product

2018-04-16 05:01:37 UTC

a.b=|a||b|/abcostheta

r=a+lamb b

2018-04-16 05:01:44 UTC

Two lines are skew when the gradients are different and they do not intercept at a point.

2018-04-16 05:02:16 UTC

Two lines are skew when the gradients are diffe

2018-04-16 05:02:21 UTC

JayWhyyy

2018-04-16 05:02:59 UTC

Bryan

2018-04-16 05:03:56 UTC

For any 2 non intersecting lines line 1 and line 2 there is a line AB that is perpendicular to both

Cheers,
Bryan

Dhinesh

2018-04-16 05:04:49 UTC

A vector equation of a straight line passing through the point
r=a+ x b

where x is a scalar parameter

Imran.

2018-04-16 05:05:06 UTC

If a.b = 0, the vectors are Perpendicular. If a.b = 1.

Acute angle between line and plane

2018-04-16 05:05:26 UTC

sin x = b.n / |b||n|

The shortest distance between two lines, two planes or a line and a plane

2018-04-16 05:06:26 UTC

2018-04-16 05:06:57 UTC

2018-04-16 05:06:58 UTC

Dot Product

19krishnag — 2018-04-16 05:08:55 UTC

a.b = |a||b|/ab cos(T)
(a,b,c).(c,d,e) = a*c + b*d + c*e

Dhinesh

2018-04-16 05:09:25 UTC

A vector equation of a straight line passing through the points C and D, with position vectors c and d respectively, is:

r=c+x(d-c)

where x is a scalar parameter

Dhinesh

2018-04-16 05:10:33 UTC

The vector equation of a plane is:

r=a+xb+yc

where:

r is the position vector of a general point in the plane
a is the position vector of a point in the plane
b and c are non-parallel, non zero vectors in the plane
x and y are scalars