Magnitude of perpindicular vectors

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The discussion focuses on finding all vectors of magnitude 4 that are perpendicular to the vector v = (-4, -2). The key equations derived are -4x - 2y = 0 and x² + y² = 16. The solution involves solving these simultaneous equations using substitution, which yields two values for y, leading to corresponding values for x. Each solution pair (x, y) represents a valid vector that meets the specified conditions.

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Homework Statement




v = (-4, -2) and need to find alll vectors of magnitude 4 that are perpindicular to v

Homework Equations





The Attempt at a Solution



I tried
let (x, y) be the vector of interest.

-4x -2y = 0
x^2 + y^2 = 16.

Is this the right track? If so, how do i solve from here?
 
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Tankertert said:

Homework Statement




v = (-4, -2) and need to find alll vectors of magnitude 4 that are perpindicular to v

Homework Equations





The Attempt at a Solution



I tried
let (x, y) be the vector of interest.

-4x -2y = 0
x^2 + y^2 = 16.

Is this the right track? If so, how do i solve from here?

Yes, right track. Just solve the simultaneous equation pair. Substitution is the easiest way. Use the first equation to get y in terms of x, then substitute into the second.

You should now get two values of y (remember to take both positive and negative square roots). Put that back into the first equation to get the corresponding values of x. Each solution (x,y) corresponds to a valid vector meeting the conditions.
 

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