Chapter 6.4, Problem 87E

To determine

To find the value of k.

Answer to Problem 87E

  $k=4$

Explanation of Solution

Given:

The vectors $\text{u}=8\text{i}+4\text{j}\text{,}\text{v}=2\text{i}-k\text{j}$ are orthogonal.

Concept used:

Two vectors u and v are orthogonal if and only if their dot product is zero.

Calculation:

Since the vectors $\text{u}=8\text{i}+4\text{j}\text{,}\text{v}=2\text{i}-k\text{j}$ are orthogonal, therefore

  $\begin{array}{l}\text{u}\cdot \text{v}=0\\ \Rightarrow \left(8\text{i}+4\text{j}\right)\cdot \left(2\text{i}-k\text{j}\right)=0\\ \Rightarrow 8\left(2\right)+4\left(-k\right)=0\\ \Rightarrow 16-4k=0\\ \Rightarrow 4k=16\\ \Rightarrow k=4\end{array}$