`A B C D` isa parallelogram with `A C\ a n d\ B D` as diagonals. Then, ` vec A C- vec B D=` `4 vec A B` b. `3 vec A B` c. `2 vec A B` d. ` vec A B`

Options

A. `4 A vec B `
B. ` 3 A vec B `
C. ` 2 A vec B `
D. `A vec B `

Answer

C

Explanation

Let ` A vec B = vec a and B vec C = vec b`
In `Delta ABC, ` we have
` A vec B + B vec C = A vec C rArr veca+ vec b = A vec C `

In ` Delta` ABD, We have
` A vec B + B vec D = A vec D rArr vec a + B vec D = vec b - vec a `
` therefore A vec C - B vec D = ( vec a + vec b ) = (vec b - vec a ) = 2 vec a = 2 A vec B `