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.

Asked by Pragya Singh | 11 months ago |  92

##### Solution :-

Let the ratio in which the point Q divides the line segment joining the

points P(3,2,-4) and R(9,8,-10) be k:1.

Using section formula,

$$(5,4,-6)= (\dfrac{k(9)+3}{k+1}, \dfrac{k(8)+2}{k+1},$$

$$\dfrac{k(-10)-4}{k+1} )$$

$$\dfrac{9k+3}{k+1}=5$$

= 9k+3 = 5k+5

= 4k = 2

$$k=\dfrac{2}{4}$$

k = $$\dfrac{1}{2}$$

Therefore, the ratio in which the point Q divides the line segment joining the points P(3,2,-4) and R(9,8,-10) is 1:2.

Answered by Pragya Singh | 11 months ago

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