Find correct to the nearest degree, the angle between p=12i - 5j and q=4i + 3j?
you know that p•q = |p|*|q|*cosθ
so plug in your numbers and solve for θ
To find the angle between two vectors, you can use the dot product formula:
θ = cos^(-1)((p · q) / (||p|| ||q||))
Where p · q is the dot product of vectors p and q, ||p|| is the magnitude of vector p, and ||q|| is the magnitude of vector q.
Let's calculate it step by step:
1. Calculate the dot product: (p · q)
p · q = (12)(4) + (-5)(3)
= 48 - 15
= 33
2. Calculate the magnitudes of the vectors: ||p|| and ||q||
||p|| = √(12^2 + (-5)^2)
= √(144 + 25)
= √(169)
= 13
||q|| = √(4^2 + 3^2)
= √(16 + 9)
= √(25)
= 5
3. Substitute the values into the formula:
θ = cos^(-1)((p · q) / (||p|| ||q||))
= cos^(-1)(33 / (13 * 5))
4. Calculate the value of cos^(-1)(33 / (13 * 5)) using a scientific calculator or trigonometric table. The result is approximately 68.5 degrees.
Therefore, the angle between vectors p=12i - 5j and q=4i + 3j is approximately 68.5 degrees.