Question

In a trapezium, if the vector `overline(BC) = lambda   overline(AD)`, `overlinep = overline(AC) + overline(BD)` is collinear with `overline(AD)` and `overlinep = mu  overline(AD)`, then ______ 

Options

• `mu = lambda + 1`

• `lambda = mu + 1`

• `lambda + mu = 1`

• `mu = 2 + lambda`

Answer 1

In a trapezium, if the vector `overline(BC) = lambda   overline(AD)`, `overlinep = overline(AC) + overline(BD)` is collinear with `overline(AD)` and `overlinep = mu  overline(AD)`, then `underline(mu = lambda + 1)`.

Explanation:

We have, `overlinep = overline(AC) + overline(BD)`

= `overline(AC) + overline(BC) + overline(CD)`

= `overline(AC) + lambda overline(AD) + overline(CD)`

= `lambda overline(AD) + (overline(AC) + overline(CD))`

= `lambda overline(AD) + overline(AD)`

= `(lambda + 1)overline(AD)`

But, `overlinep = muoverline(AD) ⇒ mu = lambda + 1`