मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the Cartesian equation of the line passing through A(1, 2, 3) and having direction ratios 2, 3, 7

Advertisements
Advertisements

प्रश्न

Find the Cartesian equation of the line passing through  A(1, 2, 3) and having direction ratios 2, 3, 7

बेरीज
Advertisements

उत्तर

The Cartesian equation of the line passing through A(x1, y1, z1) and having direction ratios a, b, c is

`(x - x_1)/a = (y - y_1)/b = (z - z_1)/c`

∴ The Cartesian equation of the line passing through A(1, 2, 3) and having direction ratios 2, 3, 7 is

`(x - 1)/2 = (y - 2)/3 = (z - 3)/7`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.6: Line and Plane - Very Short Answers

संबंधित प्रश्‍न

Find the vector equation of the line passing through the point having position vector `-2hat"i" + hat"j" + hat"k"  "and parallel to vector"  4hat"i" - hat"j" + 2hat"k"`.


Find the vector equation of line passing through the point having position vector `5hat"i" + 4hat"j" + 3hat"k"` and having direction ratios  –3, 4, 2.


Find the vector equation of the line passing through the point having position vector `hat"i" + 2hat"j" + 3hat"k"  "and perpendicular to vectors"  hat"i" + hat"j" + hat"k" and 2hat"i" - hat"j" + hat"k"`.


A(– 2, 3, 4), B(1, 1, 2) and C(4, –1, 0) are three points. Find the Cartesian equations of the line AB and show that points A, B, C are collinear.


Show that the line `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)` passes through the origin.


Find the Cartesian equation of the plane passing through A(7, 8, 6) and parallel to the XY plane.


Find the vector equation of the plane passing through the point A(– 2, 7, 5) and parallel to vector `4hat"i" - hat"j" + 3hat"k" and hat"i" + hat"j" + hat"k"`.


Find the cartesian equation of the plane `bar"r" = (5hat"i" - 2hat"j" - 3hat"k") + lambda(hat"i" + hat"j" + hat"k") + mu(hat"i" - 2hat"j" + 3hat"k")`.


Find the vector equation of the line which passes through the point (3, 2, 1) and is parallel to the vector `2hat"i" + 2hat"j" - 3hat"k"`.


Find the vector equation of the line which passes through the origin and the point (5, –2, 3).


Find the Cartesian equation of the line passing through the origin which is perpendicular to x – 1 = y – 2 = z – 1 and intersect the line `(x - 1)/(2) = (y + 1)/(3) = (z - 1)/(4)`.


Find the vector equation of the line whose Cartesian equations are y = 2 and 4x – 3z + 5 = 0.


Find the coordinates of points on th line `(x - 1)/(1) =  (y - 2)/(-2) = (z - 3)/(2)` which are at the distance 3 unit from the base point A(l, 2, 3).


The direction ratios of the line which is perpendicular to the two lines `(x - 7)/(2) = (y + 17)/(-3) = (z - 6)/(1) and (x + 5)/(1) = (y + 3)/(2) = (z - 4)/(-2)` are ______.


Find the vector equation of the plane passing through the points A(1, -2, 1), B(2, -1, -3) and C(0, 1, 5).


Solve the following :

Find the cartesian equation of the plane passing through A(1,-2, 3) and direction ratios of whose normal are 0, 2, 0.


Solve the following :

Find the cartesian equation of the plane passing through A(7, 8, 6) and parallel to the plane `bar"r".(6hat"i" + 8hat"j" + 7hat"k")` = 0.


The foot of the perpendicular drawn from the origin to a plane is M(1, 2, 0). Find the vector equation of the plane.


Solve the following :

A plane makes non zero intercepts a, b, c on the coordinate axes. Show that the vector equation of the plane is `bar"r".(bchat"i" + cahat"j" + abhat"k")` = abc.


Solve the following :

Find the vector equation of the plane passing through the point A(– 2, 3, 5) and parallel to the vectors `4hat"i" + 3hat"k" and hat"i" + hat"j"`.


Solve the following :

Find the vector equation of the plane which makes equal non zero intercepts on the coordinate axes and passes through (1, 1, 1).


Solve the following :

Find the vector equation of the plane passing through the origin and containing the line `bar"r" = (hat"i" + 4hat"j" + hat"k") + lambda(hat"i" + 2hat"j" + hat"k")`.


Find the cartesian equation of the plane passing through A(1, 2, 3) and the direction ratios of whose normal are 3, 2, 5.


Verify if the point having position vector `4hat"i" - 11hat"j" + 2hat"k"` lies on the line `bar"r" = (6hat"i" - 4hat"j" + 5hat"k") + lambda (2hat"i" + 7hat"j" + 3hat"k")`


Find the vector equation of the line passing through the point having position vector `4hat i - hat j + 2hat"k"` and parallel to the vector `-2hat i - hat j + hat k`.


Find the direction ratios of the line perpendicular to the lines

`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`


Find the Cartesian equation of the line passing through A(1, 2, 3) and B(2, 3, 4)


Find the Cartesian equation of the plane passing through the points A(1, 1, 2), B(0, 2, 3) C(4, 5, 6)


Find m, if the lines `(1 - x)/3 =(7y - 14)/(2"m") = (z - 3)/2` and `(7 - 7x)/(3"m") = (y - 5)/1 = (6 - z)/5` are at right angles


Find the Cartesian and vector equation of the plane which makes intercepts 1, 1, 1 on the coordinate axes


The point P lies on line A, B where A = (2, 4, 5} and B = (1, 2, 3). If z co-ordinate of point P is 3, the its y co-ordinate is ______.


The vector equation of the line passing through `4hati - hatj + 2hatk` and parallel to `-2hati - hatj + hatk` is ______ 


Equation of Z-axis is ______


The lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other, if ______


The centres of the circles x2 + y2 = 1, x2 + y2 + 6x – 2y = 1 and x2 + y2 – 12x + 4y = 1 are ______.


Show that the lines `(x - 1)/1 = (y - 2)/2 = (z + 1)/-1` and `x/2 = (y - 3)/2 = z/(-1)` do not intersect.


Find the direction cosines of the line `(2x - 1)/3 = 3y = (4z + 3)/2`


If vector equation of the line `(x - 2)/2 = (2y - 5)/-3 = z + 1  "is"  barr = (2hati + 5/2 hatj - hatk) + lambda (2hati - 3/2 hatj + phatk)` then p is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×