the ratio in which the yz plane divides the join of the points [-2,4.7] & [3,-5,8] is..

The coordinates of the point P which divides the line segment joining the points A (`x_1,y_1,z_1` ) and B (`x_2,y_2,z_2` ) in the ratio m:n are given by:

`((mx_2+nx_1)/(m+n),(my_2+my_1)/(m+n),(mz_2+mz_1)/(m+n))`

Now let's assume that the YZ plane divides the line segment joining the points (-2,4,7) and (3,-5,8) in the ratio k:1.

Hence the coordinates of the point of intersection are given by,

`((k(3)+(1)(-2))/(k+1),(k(-5)+1(4))/(k+1),(k(8)+(1)7)/(k+1))`

`=>((3k-2)/(k+1),(-5k+4)/(k+1),(8k+7)/(k+1))`

On the YZ plane, the x coordinate of any point is 0,

`:.(3k-2)/(k+1)=0`

`3k-2=0`

`3k=2`

`k=2/3`

Thus, the YZ plane divides the line segment formed by joining the given points in the ratio 2:3.

Comments

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