Question

Given these vectors: t=5i-4j and u=-12i-7j. What is their dot product?

Answer 1

Explanation

We are given the following vectors:

`\begin{gathered} t=5i-4j \\ u=-12i-7j \end{gathered}`

We are to determine the dot product of these vectors, i.e. t·u

We are to note that:

`\begin{gathered} i\cdot j=0 \\ i\cdot i=1 \\ j\cdot j=1 \end{gathered}`

Therefore, the dot product of the vectors can be achieved as:

`\begin{gathered} t\cdot u=(5i-4j)\cdot(-12i-7j) \\ t\cdot u=5i(-12i)+5i(-7j)-4j(-12i)-4j(-7j) \\ t\cdot u=-60(i\cdot i)-35(i\cdot j)+48(i\cdot j)+28(j\cdot j) \\ t\cdot u=-60(1)-35(0)+48(0)+28(1) \\ t\cdot u=-60+28 \\ t\cdot u=-32 \end{gathered}`

Hence, the answer is -32.