The problem involves finding the magnitude of the vector expression |2v - w| given the magnitudes of vectors v and w, and the angle between them. The context is vector mathematics, specifically focusing on vector operations and properties related to the dot product.
The discussion is ongoing with participants exploring different aspects of the problem. Some guidance has been provided regarding the use of the dot product to find the magnitude of the vector expression, but there is no explicit consensus on the next steps or a complete resolution.
There is a focus on understanding the properties of vectors and their magnitudes, with participants questioning the necessity of knowing the individual vectors to solve the problem. The discussion reflects a learning process around vector operations and definitions.
mill said:Homework Statement
If |v|=4, |w|=3 and the angle between and is pi/3, find |2v −w|
Homework Equations
##cosθ=\frac {v dot w} {|v||w|} ##The Attempt at a Solution
## 6= v dot w ##
This is as far as I got. How would I find the separate values of v and w for the equation?
ehild said:Very good! How is the absolute value of a vector defined with dot product by itself?
You do not need to know the individual vectors. You need the absolute value of 2v-w.
ehild
Start from that definition. What then is ##\sqrt{(2v-w) \cdot (2v-w)}##?mill said:u dot u = ##|u|^2## so |u|= ##\sqrt {u dot u} ## ?