Final answer:
To find the angle between two vectors, we can use the dot product and the formula cos(θ) = (→u · →v) / (|→u| |→v|). The given vectors are →u = 6→i - 9→j and →v = →i + 6→j. By plugging in the values and applying inverse cosine, we can find the angle θ.
Step-by-step explanation:
To find the angle θ between two vectors, we can use the dot product. The dot product of two vectors →u and →v is given by the equation: →u · →v = |→u| |→v| cos(θ), where |→u| and |→v| are the magnitudes of the vectors and θ is the angle between them. Rearranging the equation, we can solve for θ using the formula: cos(θ) = (→u · →v) / (|→u| |→v|).
In this case, the given vectors are: →u = 6→i - 9→j and →v = →i + 6→j. We can find →u · →v by multiplying their corresponding components and summing the resulting products: →u · →v = (6 * 1) + (-9 * 6) = -3. Next, we can find the magnitudes of →u and →v using the formula |→u| = sqrt(6^2 + (-9)^2) and |→v| = sqrt(1^2 + 6^2).
Plugging in the values, we get: cos(θ) = (-3) / (sqrt(6^2 + (-9)^2) * sqrt(1^2 + 6^2)). Using a calculator, we can find θ by taking the inverse cosine of cos(θ). Finally, we need to ensure that the angle is between 0° and 180°. If the calculated angle is greater than 180°, subtract it from 360° to obtain the corresponding angle in the range 0° to 180°.