MHB Expressing Vectors in x-y Coordinates & Calculating Magnitude & Direction

AI Thread Summary
To express vectors in x-y coordinates, the first vector V with direction π/6 and magnitude 4√3 can be calculated using x = 4√3 * cos(π/6) and y = 4√3 * sin(π/6). For vector W with direction 5π/4 and magnitude 4√2, x and y can be found similarly using the cosine and sine functions. The sum of vectors v and w can then be expressed in terms of its resultant magnitude and direction by combining their x and y components. Understanding these calculations is essential for accurately representing vectors in a two-dimensional space.
kjland
Messages
2
Reaction score
0
I'm sure this is a simple concept but i just can't wrap my brain around it, the question is:

a) Express the following vectors in terms of x-y coordinates:

i)Vector V with direction π/6 and magnitude 4√3.

ii) Vector W with direction 5π/4 and magnitude 4√2.

b) Express the vector v + w in terms of magnitude and direction.Thank you!
 
Mathematics news on Phys.org
Here's a start:

a) i) $x=4\sqrt3\cdot\cos\left(\dfrac{\pi}{6}\right)$

Can you find $y$?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top