Question

Let \( \vec{a} \) be a position vector whose tip is the point (2, -3). If \( \overrightarrow{AB} = \vec{a} \), where coordinates of A are (–4, 5), then the coordinates of B are:

• A. (-2, -2)
• B. (2, -2)
• C. (-2, 2)
• D. (2, 2)

Hint:

To find the coordinates of a point B from the given displacement vector, simply add the components of the vector to the coordinates of point A.

Answer 1

The Correct Option is C

The vector \( \overrightarrow{AB} = \vec{a} \) signifies the displacement from point A to point B. Given \( \overrightarrow{AB} = \vec{a} \), point B's coordinates are determined by adding the displacement vector \( \vec{a} \) to point A's coordinates. - The displacement vector \( \vec{a} \) has components \( \vec{a} = (2, -3) \). - Point A has coordinates \( A(-4, 5) \). Consequently, the coordinates of point B are calculated as: \[ B = A + \vec{a} = (-4, 5) + (2, -3) = (-4 + 2, 5 - 3) = (-2, 2). \]