nameVoid said:Find 2 unit vectors that make a 60 degree angle with <3,4>
Vector <a,b>
Taking b=1 cos60=1/2
3a+4=(5/2 )sqrt(a^2+1)
36a^2+96a+64=25a^2+25
11a^2+96a=-39
(sqrt(11)a+48)^2= 2265
+- a=(sqrt(2265)-48)/sqrt(11)
A unit vector is a vector with a magnitude of 1. It is often used to describe direction without considering the length of the vector.
To find a unit vector, divide a given vector by its magnitude. This will result in a vector with a magnitude of 1 and the same direction as the original vector.
The dot product is a mathematical operation that takes two vectors and produces a scalar quantity. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them.
To calculate the dot product of two vectors, multiply their corresponding components and then add the products together.
To find two unit vectors at 60 degrees, you can use the formula cos(60) = u * v / |u||v|, where u and v are the given vectors. Solve for u or v by dividing by the magnitude and then normalizing the vector to get a unit vector.