How Is the Angle Between Two Vectors Determined Using Their Dot Product?

AI Thread Summary
The angle between two vectors can be determined using their dot product formula, A·B = ABcos(theta). Given one vector of length 23 units and another of 12 units, with a scalar product of 113, the calculation proceeds as follows: 113 = 12*23*cos(theta). This simplifies to cos(theta) = 113/276, leading to theta = cos^(-1)(113/276). The resulting angle is approximately 65.8 degrees, which can be rounded to 66 degrees.
StephenDoty
Messages
261
Reaction score
0
One vector has a length of 23 units and another a length of 12 units. If the scalar product of these two vectors is 113, what is the angle between the two vectors?

A dot B = ABcos(theta)
113 = 12*23*cos(theta)
113/276= cos(theta)
cos^(-1)113/276 = theta
65.8 degrees or 66 degrees using sig figs = theta

is this right?
 
Physics news on Phys.org
yes yes
 
easy.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

The derivative of the dot product "distributes" over each vector
Replies
5
Views
666
Torque on a Circular Current Loop under a Misaligned Magnetic Field
Replies
1
Views
935
Magnetic moment and magnetic field and dot product
Replies
13
Views
2K
Dot product in uniform circular motion question -- Finding angle?
Replies
4
Views
3K
How to parametrize motion of a pendulum in terms of Cartesian coordinates?
Replies
1
Views
1K
How Do Dot Products Reflect Vector Projections?
Replies
1
Views
2K
I Angles between 4-vectors in special relativity?
Replies
5
Views
1K
Finding dot product, cross, and angle between 2 vectors
Replies
3
Views
1K
Vector product and vector product angles
Replies
4
Views
7K
I Dot product of two vector operators in unusual coordinates
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top