Question

If in ΔABC, `vec(BA) = 2veca` and `vec(BC) = 3vecb`, then `vec(AC)` is ______.

Options

• `2veca + 3vecb`

• `2veca - 3vecb`

• `3vecb - 2veca`

• `-2veca - 3vecb`

Answer 1

If in ΔABC, `vec(BA) = 2veca` and `vec(BC) = 3vecb`, then `vec(AC)` is `underlinebb(3vecb - 2veca)`.

Explanation:

By triangle law of vector addition,

`vec(AC) = vec(AB) + vec(BC)`

`vec(AC) = -vec(BA) + vec(BC)`

= `-2veca + 3vecb`

= `3vecb - 2veca`