find the angle between vectors U= <2,3> and V= <1, -5>
cos T = U dot V / ( |U|* |V| )
= (2-15) / (sqrt 13 + sqrt 26)
= -13 / (sqrt 13 + sqrt 2 sqrt 13)
= -13/ [sqrt 13 (1 + sqrt 2) ]
would that be 88 degrees, 45 degrees, 135 degrees, or 92 degrees?
To find the angle between two vectors U and V, you can use the dot product formula:
U · V = |U| * |V| * cos(theta)
where U · V is the dot product of U and V, |U| is the magnitude of U, |V| is the magnitude of V, and theta is the angle between the vectors.
Let's calculate each component:
U · V = (2 * 1) + (3 * -5) = 2 - 15 = -13
|U| = sqrt((2 * 2) + (3 * 3)) = sqrt(4 + 9) = sqrt(13)
|V| = sqrt((1 * 1) + (-5 * -5)) = sqrt(1 + 25) = sqrt(26)
Now we can substitute these values into the formula:
-13 = sqrt(13) * sqrt(26) * cos(theta)
To find cos(theta), we divide both sides of the equation by sqrt(13) * sqrt(26):
cos(theta) = -13 / (sqrt(13) * sqrt(26))
Using a calculator, we can compute the value of cos(theta) approximately as -0.9191.
Now, to find the angle theta, we can use the inverse cosine function (cos^(-1)), which gives us the angle in radians:
theta = cos^(-1)(-0.9191)
Using a calculator, we find that theta is approximately 2.7178 radians.
Therefore, the angle between vectors U and V is approximately 2.7178 radians.