In a trapezium, vector ` vec B C=alpha vec A Ddot` We will then find that ` vec p= vec A C+ vec B D` is collinear with` vec A Ddot` If ` vec p=mu vec A D ,` then which of the following is true? a) `mu=alpha+2` b) `mu+alpha=2` c) `alpha=mu+1` d) `mu=alpha+1`

Options

A. `mu= alpha +2`
B. `mu+ alpha =1`
C. `alpha = mu +1`
D. `mu =alpha +1`

Answer

D

Explanation

`vecc - vec b = alpha vecd and vecp = vec(AC) + vec(BD) = mu vec(AD)`

Hence, `vecp = vecc + vecd - vecb = mu vecd` (using `vecc - vecb = alpha vecd`)
or `alpha + 1 = mu`