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 the line passing through points having position vector `3hati + 4hatj - 7hatk and 6hati - hatj + hatk`.


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"`.


Find the vector equation of the line passing through the point having position vector `-hat"i" - hat"j" + 2hat"k"  "and parallel to the line" bar"r" = (hat"i" + 2hat"j" + 3hat"k") + λ(3hat"i" + 2hat"j" + hat"k").`


Find the cartesian equations of the line passing through A(–1, 2, 1) and having direction ratios 2, 3, 1.


Find the Cartesian equations of the line passing through A(2, 2, 1) and B(1, 3, 0).


Show that the lines given by `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1) and (x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/(4)` intersect. Also, find the coordinates of their point of intersection.


Find the Cartesian equation of the plane passing through A( -1, 2, 3), the direction ratios of whose normal are 0, 2, 5.


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 Cartesian equations of the line which passes through the point (–2, 4, –5) and parallel to the line `(x + 2)/(3) = (y - 3)/(5) = (z + 5)/(6)`.


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


Find the Cartesian equations of the line which passes through points (3, –2, –5) and (3, –2, 6).


Find the vector equation of the line which passes through the origin and intersect the line x – 1 = y – 2 = z – 3 at right angle.


Find the vector and Cartesian equations of the line passing through the point (–1, –1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z − 2.


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)`.


Choose correct alternatives:

The vector equation of line 2x – 1 = 3y + 2 = z – 2 is ______.


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(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 :

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


Solve the following :

Find the cartesian equations of the planes which pass through A(1, 2, 3), B(3, 2, 1) and make equal intercepts on the coordinate axes.


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).


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


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 Cartesian equation of the plane passing through the points (3, 2, 1) and (1, 3, 1)


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


Find Cartesian equation of the line passing through the point A(2, 1, −3) and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `hat"i" + 2hat"j" - hat"k"`


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


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 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"`


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


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 cartesian coordinates of the point on the parabola y2 = x whose parameter is ____________.


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


If the line passes through the points P(6, -1, 2), Q(8, -7, 2λ) and R(5, 2, 4) then value of λ 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 line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ – plane at the point `(0, 17/2, (-13)/2)`, then ______.


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


If the line `(x - 1)/2 = (y + 1)/3 = z/4` lies in the plane 4x + 4y – kz = 0, then the value of k is ______.


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×