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

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 between parallel lines:

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


What are the points on the y-axis whose distance from the line  `x/3 + y/4 = 1` is 4 units.


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


Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x– 7y + 5 = 0 and 3x + y = 0.


Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.


A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.


Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle tan−1 \[\left( \frac{5}{12} \right)\] with the positive direction of x-axi .


A line passes through a point A (1, 2) and makes an angle of 60° with the x-axis and intersects the line x + y = 6 at the point P. Find AP.


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


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.


Find the distance of the point of intersection of the lines 2x + 3y = 21 and 3x − 4y + 11 = 0 from the line 8x + 6y + 5 = 0.


Show that the product of perpendiculars on the line \[\frac{x}{a} \cos \theta + \frac{y}{b} \sin \theta = 1\]  from the points \[( \pm \sqrt{a^2 - b^2}, 0) \text { is }b^2 .\]


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:

4x − 3y − 9 = 0 and 4x − 3y − 24 = 0


Determine the distance between the pair of parallel lines:

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


Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, −1).

Answer 3:


Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y= 6.


Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y+ 5 = 0, whose distance from the point(3, 2) is 7/5.


If the lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0 are concurrent, then write the value of 2abc − ab − bc − ca.


Write the locus of a point the sum of whose distances from the coordinates axes is unity.


The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio


The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is


The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point 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


If the tangent to the curve y = 3x2 - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are


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


Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.


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


A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:


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)`


The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.


The distance of the point (-3, 2, 3) from the line passing through (4, 6, -2) and having direction ratios -1, 2, 3 is ______units.


The distance between the parallel lines 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0 is `a/b`. Value of a + b is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×