Home
Class 12
MATHS
If A(3,2,-4),B(5,4,-6)a n dC(9,8,-10) ar...

If `A(3,2,-4),B(5,4,-6)a n dC(9,8,-10)` are three collinear points, then find the ratio in which point `C` divides `A Bdot`

Text Solution

Verified by Experts

Let C divides AB in the ratio `lamda:1`. Then
`" "C-=((5lamda+3)/(lamda+1),(4lamda+2)/(lamda+1), (-6lamda-4)/(lamda+1))=(9, 8, -10)`
Comparing, we get
`" "5lamda+3=9lamda+9 or 4lamda=-6 or lamda=-3//2`
Also, from `4lamda+2=8lamda+8 and -6lamda-4=-10lamda-10`, we get the same value of `lamda`.
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

Using section formula, show that the points A (3 , 2 , -4) , b ( 5 , 4 , -6) and C ( 9 , 8 , -10) are collinear . Also find the ratio in which the point B divides the line-segment overline(AC) .

Show that the points A ( 3 , 2 , -4) , B ( 5 , 4 , -6) and C ( 9 , 8 , -10) are collinear. Also find the ratio in which C divides the line-segment overline(AB) .

Given that P (3,2,-4), Q (5,4,-6) & R (9,8,-10) are collinear. Find the ratio in which Q divides PR

Given that P(3,2,-4) Q(5,4-6) and R(9,8,-10) are collinear find the ratio in which Q divides PR

Show that the points A(1,-2,-8),B(5,0,-2)a n dC(11,3,7) are collinear, and find the ratio in which B divides A Cdot

Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , and find the ratio in which B divides AC.

If A(2,-1)a n dB(6,5) are two points, then find the ratio in which the foot of the perpendicular from (4,1) to A B divides it.

If A(-2,1),B(2,3)a n dC(-2,-4) are three points, find the angle between B Aa n dB Cdot

If the points P (1,2,3), Q(4,5,6) and R(7,8,9) are collinear then Q divides PR in the ratios of -

A (4,6) , B (-1,3) and C(2,-2) are three given points . Find the following : coordinates of the point equidistant from A,B,C and the distance of this point from A,B,C.