Finding the angle between 2 vectors

1. May 17, 2004

PinkFlamingo

Could someone refresh my memory how to find the angle between 2 vectors in 3d, say:

a= 4i + j + 2k
b= -i +2j + k

Thanks!

2. May 17, 2004

enigma

Staff Emeritus
dot product

a.b = |a||b|cos (ang)

3. May 17, 2004

PinkFlamingo

So how would I find the angle for the two I posted?

4. May 17, 2004

He just told you. Solve for theta and plug and chug.

$$\theta = \arccos{\left( \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|\right)}$$

$$\vec{a}\cdot\vec{b} = a_1b_1 + a_2b_2 + a_3b_3$$
and
$$|\vec{a}| = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2}$$

if $\vec{a} = <a_1,a_2,a_3>$ and likewise for b.

Last edited: May 17, 2004
5. May 17, 2004
The text passage contains a mathematical question about finding the angle between two vectors in 3D space, and it also provides the method to solve the problem, including the formula and the steps to calculate the angle.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Finding the angle between 2 vectors

1. May 17, 2004

PinkFlamingo

Could someone refresh my memory how to find the angle between 2 vectors in 3d, say:

a= 4i + j + 2k
b= -i +2j + k

Thanks!

2. May 17, 2004

enigma

Staff Emeritus
dot product

a.b = |a||b|cos (ang)

3. May 17, 2004

PinkFlamingo

So how would I find the angle for the two I posted?

4. May 17, 2004

He just told you. Solve for theta and plug and chug.

$$\theta = \arccos{\left( \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|\right)}$$

$$\vec{a}\cdot\vec{b} = a_1b_1 + a_2b_2 + a_3b_3$$
and
$$|\vec{a}| = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2}$$

if $\vec{a} = <a_1,a_2,a_3>$ and likewise for b.

Last edited: May 17, 2004
5. May 17, 2004
user
The text passage contains a mathematical question about finding the angle between two vectors in 3D space, and it also provides the method to solve the problem, including the formula and the steps to calculate the angle.

TYPE: SINGLE_QUESTION_WITH_ANSWER