Question

If the direction ratios of a line passing through two points P (1,4,5) and Q (2, 3,K) are (2, -2, 4) then find the value of K?
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Answer 1

We know that direction ratios of a line joining two points \((x_1,y_1z_1)\) and$(x_2,y_2,z_1)$ is given by $(x_2-x_1,y_2-y_1{z}_2-z_1)$
Here, $x_1=1,y_1=4,z_1=5\&x_2=2,y_2=3,z_2=K$
So, the direction ratios can be given by
( (2-1) , (3 - 4) , (K - 5) )
Or (1, -1 , K - 5 )
Now let’s compare these direction ratios with the direction ratios given in the question.
Oops! it’s not matching. Wait ! we know that direction ratios can be many. If we multiply direction ratios by some number we get another set of direction ratios.
By observation we can tell that the direction ratios given in the question are multiplied by “2” to the direction ratios we have got.
So we’ll multiply these direction ratio by “2” to compare -
(2, -2 , 2 ( K - 5) )
On comparing we get 2(K -5) = 4
Or K = 7