Mathematics: What is the angle θab between a⃗ and b⃗ ? express your answer using one significant figur?

What is the angle θab between a⃗ and b⃗ ? express

Ответ:

bandzlvr

12.03.2022

If you have to find the angle between two vectors, first of all, you should draw them with their beginnings at the common point. Then the smallest of two possible angles is the angle between these vectors (see attached diagram for details).

Now, use the definition of dot product:

$\vec{a}\cdot \vec{b}=|\vec{a}|\cdot |\vec{b}|\cdot \cos \theta_{\vec{a},\vec{b}}.$

Express the cosine from the previous expression:

$\cos \theta_{\vec{a},\vec{b}}=\dfrac{\vec{a}\cdot \vec{b}}{|\vec{a}|\cdot |\vec{b}|}.$

Moreover, if $\vec{a}=(a_1,a_2,a_3)$ and $\vec{b}=(b_1,b_2,b_3),$ then

$\cos \theta_{\vec{a},\vec{b}}=\dfrac{a_1\cdot b_1+a_2\cdot b_2+a_3\cdot b_3}{\sqrt{a_1^2+a_2^2+a_3^2}\cdot \sqrt{b_1^2+b_2^2+b_3^2}}.$

What is the angle θab between a⃗ and b⃗ ? express your answer using one significant figur?

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What is the angle θab between a⃗ and b⃗ ? express your answer using one significant figur?

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