Video Transcript
If vector ππ is equal to π’ minus two π£ and vector π equals four, three, then the coordinates of vector π are blank.
We begin by recalling that vector ππ is equal to vector π minus vector π. We also know that any vector π written in terms of unit vectors π’ and π£ such that π is equal to π₯π’ plus π¦π£ can be rewritten such that vector π has components π₯ and π¦. The vector π’ minus two π£ can, therefore, be rewritten in terms of its components as one, negative two. This must be equal to the vector four, three minus the vector π₯, π¦ where π₯ and π¦ are the components of vector π.
We recall that when adding and subtracting vectors, we simply add or subtract the corresponding components. When considering the π₯-components, we have the equation one is equal to four minus π₯. Adding π₯ and subtracting one from both sides of this equation gives us π₯ is equal to four minus one. This gives us a value of π₯ equal to three. Repeating this for our π¦-components, we have the equation negative two is equal to three minus π¦. We can then add π¦ and two to both sides of this equation such that π¦ is equal to three plus two. This gives us a π¦-component equal to five.
Vector π, therefore, has coordinates three, five.
