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
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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!
 
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Here's a start:

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

Can you find $y$?
 
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