Question Video: Expressing a Vector in Terms of the Standard Unit Vectors given Its Magnitude and Direction Mathematics • First Year of Secondary School

Video Transcript

A body moved 190 centimeters due east, where 𝐢 and 𝐣 are two unit vectors in the east and north directions, respectively. Express its displacement in terms of the two unit vectors 𝐢 and 𝐣.

We’ve been told that unit vector 𝐢 represents the easterly direction and unit vector 𝐣 the northerly direction. Let’s call our displacement vector 𝐃, which in terms of the unit vectors 𝐢 and 𝐣 will be of the form 𝑎𝐢 plus 𝑏𝐣. We know that the body moved due east, which tells us that the vector expressing the displacement will have no northerly component. This means that the coefficient of unit vector 𝐣 will be zero. That is, the component or coefficient 𝑏 is equal to zero. We know that the body moved 190 centimeters in the easterly direction. So the coefficient of 𝐢, that’s 𝑎, will be 190. Hence, the displacement of the body can be written as 190𝐢 plus zero 𝐣, which is 190𝐢 centimeters.