The projection of the line joining the ponts `(3,4,5)` and `(4,6,3)` on the line joining the points (-1,2,4) and (1,0,5) is

Options

A. `4/3`
B. `2/3`
C. `1/3`
D. `1/2`

Answer

A

Explanation

The direction of the line joining `P(-1,2,4)` and `Q(1,0,5)` are proportional to 2,-2,1
`:.` It is direction cosines are `2/3,-2/3,1/3`
Thus, the projection of the line joining `A(3,4,5)` and `B(4,6,3)` on `PQ` is given by
`|(4-3)xx2/3+(6-4)xx(-2/3)+(3-5)xx1/3|=|2/3-4/3-2/3|=4/3`