Final answer:
The cosine angle between p and q is 0.663. The magnitude of p is √(62) and the magnitude of q is √(50). The scalar product of p and q is 37.
Step-by-step explanation:
(i) To find the cosine angle between p and q, we need to calculate the dot product of p and q and divide it by the product of their magnitudes. The dot product of p and q is given by:
p · q = 7*4 + 3*5 + 2*(-3) = 28 + 15 - 6 = 37
The magnitude of p is given by:
|p| = √(7² + 3² + 2²) = √(62)
The magnitude of q is given by:
|q| = √(4² + 5² + (-3)²) = √(50)
Thus, the cosine angle between p and q is given by:
cosθ = (p · q) / (|p| * |q|) = 37 / (√(62) * √(50)) = 37 / √(3100) = 37 / 55.77 ≈ 0.663
(ii) The magnitude of p is |p| = √(7² + 3² + 2²) = √(62).
(iii) The magnitude of q is |q| = √(4² + 5² + (-3)²) = √(50).
(iv) The scalar product of p and q is given by:
p · q = 7*4 + 3*5 + 2*(-3) = 28 + 15 - 6 = 37.