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.
