हिंदी

Find the Co-ordinates of the Point, Which Divides the Line Segment Joining the Points A(2, − 6, 8) and B(− 1, 3, − 4) Externally in the Ratio 1 : 3 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.

Advertisements

उत्तर

Let `bara` and `barb` be the position vectors of the points A and B respectively.

Then, `bara = 2hati −6hatj + 8hatk` and `barb = −hati +3hatj −4hatk`

Let R( `barr` ) be the point which divides the line segment joining the points A and B externally in the ratio 1 : 3.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2012-2013 (October)

APPEARS IN

संबंधित प्रश्न

Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).


Find the distance between parallel lines:

15x + 8y – 34 = 0 and 15x + 8y + 31 = 0


Find the distance between parallel lines  l (x + y) + p = 0 and l (x + y) – r = 0


Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).


Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.


Find the distance of the point (2, 3) from the line 2x − 3y + 9 = 0 measured along a line making an angle of 45° with the x-axis.


Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope 3/4.


Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x − 2y = 1.


Find the distance of the line 2x + y = 3 from the point (−1, −3) in the direction of the line whose slope is 1.


The perpendicular distance of a line from the origin is 5 units and its slope is − 1. Find the equation of the line.


Find the equation of a line perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and at a distance of 3 units from the origin.


Find the distance of the point (4, 5) from the straight line 3x − 5y + 7 = 0.


Show that the perpendiculars let fall from any point on the straight line 2x + 11y − 5 = 0 upon the two straight lines 24x + 7y = 20 and 4x − 3y − 2 = 0 are equal to each other.


Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]


If sum of perpendicular distances of a variable point P (xy) from the lines x + y − 5 = 0 and 3x − 2y + 7 = 0 is always 10. Show that P must move on a line.


If the length of the perpendicular from the point (1, 1) to the line ax − by + c = 0 be unity, show that \[\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2ab}\] .

 


Determine the distance between the pair of parallel lines:

8x + 15y − 34 = 0 and 8x + 15y + 31 = 0


The equations of two sides of a square are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the area of the square.

 


If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sin θ, − cos θ) lies on the line y = 2x, then write the value of tan θ.


Write the value of θ ϵ \[\left( 0, \frac{\pi}{2} \right)\] for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.


L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through


The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.


Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is


The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 is


The shortest distance between the lines

`bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda (hat"i" - hat"j" + hat"k")` and

`bar"r" = (2hat"i" - hat"j" - hat"k") + mu(2hat"i" + hat"j" + 2hat"k")` is


Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.


The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.


A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.


If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.


The distance between the lines y = mx + c1 and y = mx + c2 is ______.


A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is ______.


The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.


The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are

Column C1 Column C2
(a) Parallel to y-axis is (i) λ = `-3/4`
(b) Perpendicular to 7x + y – 4 = 0 is (ii) λ = `-1/3`
(c) Passes through (1, 2) is (iii) λ = `-17/41`
(d) Parallel to x axis is λ = 3

Find the length of the perpendicular drawn from the point P(3, 2, 1) to the line `overliner = (7hati + 7hatj + 6hatk) + λ(-2hati + 2hatj + 3hatk)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×