Question Video: Expressing a Vector in Terms of the Two Unit Vectors 𝐢 and 𝐣 Mathematics • First Year of Secondary School

Video Transcript

Using that each square of the grid has length one, write the vector 𝐀𝐁 in the form 𝑎𝐢 plus 𝑏𝐣 and then in the form 𝑎, 𝑏.

From the start point 𝐴, we move plus two units in the horizontal direction, which represents the vector two 𝐢. We then move positive three units in the vertical direction, which represents the vector three 𝐣, to reach the point 𝐵. The vector 𝐀𝐁, which represents traveling directly from 𝐴 to 𝐵, is then the sum of these unit vectors, and that’s two 𝐢 plus three 𝐣. The components 𝑎 and 𝑏 are therefore two and three, respectively. And so we have 𝐀𝐁 is two 𝐢 plus three 𝐣 in terms of unit vectors and two, three in component form.