Home
Class 12
MATHS
Find the point of intersection of AB ...

Find the point of intersection of AB and `A(` 6,-7,0),B(16,-19,-4,) , C(0,3,-6) and D(2,-5,10).

Text Solution

Verified by Experts

Let AB and CD intersect at P.
Let P divides AB in ratio `lamda:1` and CD in ratio `mu:1`.
Then coordinates of P are `((16lamda+6)/(lamda+1), (-19lamda-7)/(lamda+1), (-4lamda)/(lamda+1))or ((2mu)/(mu+1), (-5mu+3)/(mu+1), (10mu-6)/(mu+1))`
Comparing we have `lamda=-(1)/(3) or mu=1`.
Using these values, we get point of intersection as (1, -1, 2).
Here it is also proved that lines AB and CD intersect of points A, B, C and D are coplanar.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 20|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 21|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 18|1 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|541 Videos

Similar Questions

Explore conceptually related problems

Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10) are such that AB and CD intersect at the point P(1,-1,2) .

Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y^2+16x+12y+c=0 at a point Q , then the coordinates of Q are (A) (-6,-11) (B) (-9,-13) (C) (-10,-15) (D) (-6,-7)

The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1 and (x+3)/(-36)=(y-3)/2=(z-6)/4 is (A) (21 ,5/3,(10)/3) (B) (2,10 ,4) (C) (-3,3,6) (D) (5,7,-2)

If the coordinates of the points A,B,C,D be (1,2,3), (4,5,7), (-4,3,-6) and (2,9,2) respectively, then find the angle between the lines AB and CD.

Determine the matrices A and B, where A+2B={:[(1,2,0),(6,-3,3),(-5,3,1)] and 2A-B={:[(2,-1,5),(2,-1,6),(0,1,2)]:} .

The points A,B,C,D have the respective coordinates (-2,-3),(6,-5) , (18,9) and (0,12) . Find the area of the quadrilateral ABCD.

Find the equation of the line passing through the points A(0,6,-9) and B(-3,-6,3). If D is the foot of the perpendicular drawn a point C(7,4,-1) on the line AB, then find the coordinates of the point D and the equation of line CD.

Find x such that the four points A(3,2,1), B(4,x,5), C(4,2,-2) and D (6,5,-1) are coplanar .

A straight line with slope 2 and y-intercept 5 touches the circle x^2+y^2+16 x+12 y+c=0 at a point Q . Then the coordinates of Q are (a) (-6,11) (b) (-9,-13) (c) (-10 ,-15) (d) (-6,-7)

The reflection of the point (4,-13) about the line 5x+y+6=0 is a. (-1,-14) b. (3,4) c. (0,-0) d. (1,2)