Question :
1)Find the perpendicular distance of a point C=c fron the straight line (r-a)^b =0
2) Find the shortest distance between the two skew lines (r-a)^b =0 and (r-c)^d =
Could you please help me solving this? I dont understand how to get started as there is no point given as passing the given line or given as pararrel
If (r-a)×b = 0 then (r-a) and b must be parallel, since the sine of the angle between them is zero.
As for the 2nd one, if you meant to say that (r-a)×d = 0 as well, then b and d are parallel. What do you know about the distance between parallel lines in 3D?
I'm not familiar with the notation (r-a)^b = 0
as it relates to vectors. Care to explain a bit more?
(r-a)^b = 0 : ^ refers to the cross product , as i know cross product gives a vector perpendicular to both given vectors
To find the perpendicular distance of a point C from a straight line, we need to calculate the shortest distance between the point and the line. Here's how you can get started:
1) Find the equation of the given straight line:
The equation (r - a)^b = 0 represents a straight line. However, we need more information to find the equation of the line. Specifically, we need the values of a and b. Once you have those values, you can determine the equation of the line.
For example, if we have the equation (r - 2)^3 = 0, it represents a line passing through the point (2, 0). In this case, a = 2 and b = 3.
2) Find the equation of the line perpendicular to the given line:
The equation of a line perpendicular to a given line can be found by using the negative reciprocal of the slope of the given line. If the equation of the given line is in the form y = mx + c, where m is the slope, the equation of the perpendicular line will be -1/m.
If the equation of the given line is not explicitly given in terms of x and y, you might need to convert it to this form by isolating y. Then you can determine the slope and find the equation of the perpendicular line.
3) Find the intersection point between the given line and the perpendicular line:
To find the intersection point between two lines, you need to solve their equations simultaneously. By solving the equations, you will get the coordinates of the intersection point.
4) Calculate the distance between point C and the intersection point:
Once you have the coordinates of the intersection point and the coordinates of point C, you can calculate the distance between them using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
(x1, y1) are the coordinates of the intersection point, and (x2, y2) are the coordinates of point C.
For the second question regarding the shortest distance between two skew lines, we also need more information. The equations provided (r - a)^b = 0 and (r - c)^d = 0 do not explicitly define the lines or their orientation. If you have additional information about the lines, such as a common point or a parallel direction, please provide that information, and I can assist you further.