Question Video: Evaluating Expressions Involving the Addition of Given Vectors Mathematics • Third Year of Secondary School

Video Transcript

If vector 𝚨 is equal to four 𝐢 plus two 𝐣 plus three 𝐤 and vector 𝚩 is equal to two 𝐢 plus three 𝐣 plus four 𝐤, find vector 𝚨 plus vector 𝚩.

We recall that when adding two vectors, we simply add their corresponding components. In this question, we begin by adding the 𝐢-components. Four 𝐢 plus two 𝐢 is equal to six 𝐢. Adding the 𝐣-components gives us five 𝐣 as two 𝐣 plus three 𝐣 is five 𝐣. Finally, adding the 𝐤-components gives us seven 𝐤. Vector 𝚨 plus vector 𝚩 is equal to six 𝐢 plus five 𝐣 plus seven 𝐤, where 𝐢, 𝐣, and 𝐤 are the unit vectors in the 𝑥-, 𝑦-, and 𝑧 direction, respectively.