Angles (direction) in Vector Calculus

[darkphoenix]

Not a specific question, but how exactly do you know when to use dot product and to find the angle between two vectors or

Or should it yield the same angle? And how do you know whether to subtract the answer from 90 degrees or 180?

Do we just need to try and visualise it?

[jasoN-]

The dot product angle formula is more useful in most cases,
as the one applies to vectors with horizontal/vertical components, also only i and j components. (eg 3i+5j)
The freedom of the dot product angle formula allows the angle between 3D vectors to be solved. (eg. 3i+5j+2k)
Your best bet is to stick with the dot product angle formula.
is usually used in complex numbers (Real and Im axes), and usually doesn't apply to vectors.

Also for the 90/180 degrees thing, its mainly the context that matters.
If a question asks for an acute angle between, say, the diagonals of a parallelogram, the formula may help if you find yourself solving for the obtuse angle.
Yes visualising/drawing a rough sketch will help in determining whether or not you would need to subtract such angles, however as vectors don't need to take into account the origin (free floating, starting point doesn't matter), the dot product angle formula is pretty full proof.

[tram]

wow.....looks like we have a new martoman.......

nice explantion dude (Y)

you seem to thouhgoughly understand your stuff.....how'd you only get a 39 last year??

[jasoN-]

lol, I cant even compare myself to Martoman (actually I can, it's a large margin of difference). I was just making stuff up that made sense while i was typing.
And, I only got 39 cos i didn't realise vce was that important , just winged my way through it and only did ~5-6 exams.
if i knew how much of an advantage doing a 3/4 in year 11 was, i woulda went all out.

[darkphoenix]

Ah ok thanks dude!

[Mao]

To add:

The dot product is used to find the angle between two vectors.

The tangent method is used to find the angle from the horizontal axis in a 2D space.

You will also learn that for a vector in 3D that , , where alpha, beta and gamma are angles made with the x, y and z axis.

[darkphoenix]

Nice thanks Mao!

But if you were to dot a vector with , then this would be the same as finding the angle it makes with the horizontal axis for 2D, correct?

[Mao]

Exactly right. If you dot a vector with any unit coordinate vectors (i, j or k), you'll find the angle it makes with the axes (thus the cos relationship with x, y and z axis in 3D). However, these forms all involve the magnitude of the vector.

Whereas for the tangent method, you don't use the magnitude, you use the size of the components.

[darkphoenix]

Ok cool thanks again.

[tram]

To add:

The dot product is used to find the angle between two vectors.

The tangent method is used to find the angle from the horizontal axis in a 2D space.

You will also learn that for a vector in 3D that , , where alpha, beta and gamma are angles made with the x, y and z axis.

is that assumed spech knowledge??

[fady_22]

To add:

The dot product is used to find the angle between two vectors.

The tangent method is used to find the angle from the horizontal axis in a 2D space.

You will also learn that for a vector in 3D that , , where alpha, beta and gamma are angles made with the x, y and z axis.

is that assumed spech knowledge??

It's in the Essentials text.

[tram]

did not know that.......... >.<

[darkphoenix]

did not know that.......... >.<

Same, our school has to used shitty maths quest.

[tram]

lol...... well i USE essentials.......... i've just forgotten all about vectors >.< learning about vector spaces in umep has really put me off vectors....... >.<

beta get onto the spech revision......

[darkphoenix]

LOL Essentials is soo hard though, so depressing when you cant do so many of the questions.