Question

During a cricket match, the position of the bowler, the wicket-keeper, and the leg slip fielder are in a line given by `vecB = 2hati + 8hatj, vecW = 6hati + 12hatj, and vecF = 12hati + 18hatj` respectively. Calculate the ratio in which the wicket keeper divides the line segment joining the bowler and the leg slip fielder.

Answer 1

`veca = 2hati + 8hatj`

`vecb = 12hati + 18hatj`

Let the ratio be λ : 1 

By using the section formula

Position vector of W = `(m  vecb + n  veca)/(m + n)`

m = λ, and n = 1

`(6hati + 12hatj) = (λ(12 hati + 18 hatj) + (2 hati + 8 hatj))/(λ + 1)`

⇒ `6hati + 12hatj = ((12 λ + 2)i)/(λ + 1) + ((18 λ + 8)j)/(λ + 1)`

Comparing both sides

6 = `(12 λ + 2)/(λ + 1)`

6 λ + 6 = 12 λ + 2

4 = 6 λ

`λ/1 = 4/6`

= `2/3`

So, the required ratio is 2 : 3.