- #1
hazellaw
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how to find two vectors that make an angle of 60O with v=<3,4>??
can i let b=<x,y>, then
cos60=(3x+4y)/5sqrt(x2+y2)
5sqrt(x2+y2)=3x+4y
can i let b=<x,y>, then
cos60=(3x+4y)/5sqrt(x2+y2)
5sqrt(x2+y2)=3x+4y
Find Vectors to Make 60° Angle w/ v=<3,4>
- Thread starter hazellaw
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In summary, to find two vectors that make an angle of 60 degrees with v=<3,4>, you can use the formula cos60=(3x+4y)/5sqrt(x2+y2) after letting b=<x,y>. However, it may be easier to use <cosθ,sinθ>, write <3,4> in polar form, or find the line perpendicular to <3,4> and go along it the appropriate distance.
- #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!
Hi hazellaw! Welcome to PF!
(have a square-root: √ and a degree: º)
That'll certainly do it.
But easier would be
i] use <cosθ,sinθ> instead of <x.y>
or ii] write <3,4> in polar form (r,θ)
or iii] find the line perpendicular to <3,4>, and go along it the appropriate distance.
Hi hazellaw! Welcome to PF!
(have a square-root: √ and a degree: º
)hazellaw said:
That'll certainly do it.
But easier would be
i] use <cosθ,sinθ> instead of <x.y>
or ii] write <3,4> in polar form (r,θ)
or iii] find the line perpendicular to <3,4>, and go along it the appropriate distance.
Related to Find Vectors to Make 60° Angle w/ v=<3,4>
1. What is the formula for finding the angle between two vectors?
The formula for finding the angle between two vectors is: cosθ = (a · b) / (|a| * |b|), where a and b are the two vectors and θ is the angle between them.
2. How do I find the magnitude of a vector?
The magnitude (or length) of a vector can be found by using the Pythagorean theorem, where the magnitude is the square root of the sum of the squares of the vector's components. In this case, the magnitude of vector v = <3,4> is √(3² + 4²) = √25 = 5.
3. What is the significance of a 60° angle in vector mathematics?
A 60° angle is significant in vector mathematics because it is considered a special angle that can be easily calculated using trigonometric functions. It is also the angle at which the cosine function has a value of 0.5, making it a commonly used angle in various calculations.
4. How do I find a vector that makes a 60° angle with a given vector?
To find a vector that makes a 60° angle with a given vector, you can use the formula for finding the angle between two vectors and solve for one of the vectors. In this case, the vector that makes a 60° angle with v = <3,4> would be <5,3> or <5,-3>, as long as the magnitudes of the two vectors are the same.
5. Can I use any two vectors to create a 60° angle?
No, not all pairs of vectors can create a 60° angle. The two vectors must have equal magnitudes and the angle between them must be 60°. Additionally, the dot product of the two vectors must be positive, meaning the two vectors are pointing in the same general direction.
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