Video Transcript
Given 𝐀𝐁 is equal to negative
one, negative three, zero and vector 𝐀 is equal to negative four, negative five,
negative five, express vector 𝐁 in terms of the fundamental unit vectors.
We recall that when finding the
vector between two points, vector 𝐀𝐁 is equal to vector 𝐁 minus vector 𝐀. If we let vector 𝐁 have components
𝑥, 𝑦, 𝑧, then negative one, negative three, zero is equal to 𝑥, 𝑦, 𝑧 minus
negative four, negative five, negative five. Adding vector 𝐀 to both sides of
this equation gives us negative one, negative three, zero plus negative four,
negative five, negative five is equal to 𝑥, 𝑦, 𝑧.
When adding and subtracting
vectors, we can look at each component separately. This means that 𝑥 is equal to
negative one plus negative four. This is the same as negative one
minus four, which is equal to negative five. 𝑦 is equal to negative three plus
negative five. This equals negative eight. Finally, 𝑧 is equal to negative
five. Vector 𝐁 is, therefore, equal to
negative five, negative eight, negative five.
We were asked to write vector 𝐁 in
terms of the fundamental unit vectors. This means we need to write it in
the form 𝑥𝐢 plus 𝑦𝐣 plus 𝑧𝐤. Vector 𝐁 is, therefore, equal to
negative five 𝐢 minus eight 𝐣 minus five 𝐤.
