Question

what is vector equation of line

Answer 1

Any vector in 2-dimensional space has the property of x^2+y^2=v with an angle theta derived from arctan. It's similar to a right triangle where when you draw any linear equation (or a line) with coordinates (x, y), you can draw a right triangle. The difference between a vector and an ordinary line is that it measures angle as well. So use arctan to find the angle. I hope this helps! If not, you can reply back.

Answer 2

r= ai + bj + ck + t(di + ej + fk) where a,b,c,d,e,f are constants and i, j , k are the versors of a Cartesian coordinate system. we can say it represents x y and z in 3-dimensional space.

Answer 3

*t is the scalar product

Answer 4

thanks

Answer 5

and plz explain what is eqation of plane

Answer 6

The standard equation of a plane in 3 space is
Ax + By + Cz + D = 0
The normal to the plane is the vector (A,B,C).


Given three points in space (x1,y1,z1), (x2,y2,z2), (x3,y3,z3) the equation of the plane through these points is given by the following determinants.


Expanding the above gives
A = y1 (z2 - z3) + y2 (z3 - z1) + y3 (z1 - z2)
B = z1 (x2 - x3) + z2 (x3 - x1) + z3 (x1 - x2)
C = x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2)
- D = x1 (y2 z3 - y3 z2) + x2 (y3 z1 - y1 z3) + x3 (y1 z2 - y2 z1)

Note that if the points are colinear then the normal (A,B,C) as calculated above will be (0,0,0).

The sign of s = Ax + By + Cz + D determines which side the point (x,y,z) lies with respect to the plane. If s > 0 then the point lies on the same side as the normal (A,B,C). If s < 0 then it lies on the opposite side, if s = 0 then the point (x,y,z) lies on the plane.