# Angle between resultant and vector

• B

## Main Question or Discussion Point

Can we find the angle between resultant and one of its vectors without breaking into components?

sophiecentaur
Gold Member
You have to use some co ordinate system but Cartesian is not necessary. Working out the sides and angles of a triangle, given a side, side and included angle is basic trig. so you don't have to use components. But 20 million flies can't be wrong and using components is usually the most convenient way. • Gurasees
ZapperZ
Staff Emeritus
Can we find the angle between resultant and one of its vectors without breaking into components?
Sure, if you think using sine and cosine laws are easier. It usually isn’t.

This is also a math question, not physics.

Zz.

• Gurasees
A.T.
Can we find the angle between resultant and one of its vectors without breaking into components?
How are the vectors given, if not as components? How many vectors are added to get the resultant vector?

• Gurasees
Svein
Can we find the angle between resultant and one of its vectors without breaking into components?
Mathematically yes, since the angle between the vectors A and B is given by $\cos(\phi)=\frac{\vec{A}\cdot \vec{B}}{\vert \vec{A}\vert\vert \vec{B}\vert}$. Calculating the inner product of two vectors is left as an assignment for the student.

• Gurasees
You have to use some co ordinate system but Cartesian is not necessary. Working out the sides and angles of a triangle, given a side, side and included angle is basic trig. so you don't have to use components. But 20 million flies can't be wrong and using components is usually the most convenient way. Thank you

Mathematically yes, since the angle between the vectors A and B is given by $\cos(\phi)=\frac{\vec{A}\cdot \vec{B}}{\vert \vec{A}\vert\vert \vec{B}\vert}$. Calculating the inner product of two vectors is left as an assignment for the student.
Thank you