Video Transcript
Express vector 𝐀 which is equal to one, negative six, four in terms of fundamental unit vectors.
We begin by recalling that the fundamental unit vectors are denoted 𝐢 hat, 𝐣 hat, and 𝐤 hat. These can be shown on the three-dimensional coordinate plane as follows. The unit vector in the 𝑥-direction is denoted 𝐢 hat, the unit vector in the 𝑦-direction is denoted 𝐣 hat, and the unit vector in the 𝑧-direction is denoted 𝐤 hat.
We are told in this question that vector 𝐀 moves one unit in the 𝑥-direction, negative six units in the 𝑦-direction, and four units in the 𝑧-direction. This means that vector 𝐀 is equal to one 𝐢 minus six 𝐣 plus four 𝐤. Simplifying this, we get 𝐀 is equal to 𝐢 minus six 𝐣 plus four 𝐤.
