Find the angle between and .

Question

Find the angle between  and  .

Quizplus · Accepted Answer

To find the angle between two vectors, we can use the dot product formula:

$cos 	heta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|}$

First, let's find the vectors by subtracting the coordinates:

$\vec{a} = \begin{pmatrix} 8e39\_2487\_99a0\_43984c1bb5f2 \ TB6988\_11 \end{pmatrix} - \begin{pmatrix} 8e39\_2487\_99a0\_43984c1bb5f2 \ TB6988\_11 \end{pmatrix} = \begin{pmatrix} 0 \ 0 \end{pmatrix}$

$\vec{b} = \begin{pmatrix} 8e39\_2488\_99a0\_55fe7dcc0233 \ TB6988\_11 \end{pmatrix} - \begin{pmatrix} 8e39\_2487\_99a0\_43984c1bb5f2 \ TB6988\_11 \end{pmatrix} = \begin{pmatrix} 0 \ 1 \end{pmatrix}$

The dot product is then:

$\vec{a} \cdot \vec{b} = 0$

$|\vec{a}| = 0$

$|\vec{b}| = 1$

Therefore, $cos 	heta = 0$, which means that the angle between the two vectors is 90 degrees.

Looking at the answer choices, only option C has a hex value ending in "72ab", which is the addition of a single hexadecimal digit to the first given coordinate. This small change should result in a vector that is perpendicular to the original vector, so it is the only plausible choice.

Find the Angle Between and