Final answer:
To evaluate the expressions for vectors u and v: a. find the dot product by multiplying corresponding components and adding the products. b. multiply their magnitudes. c. calculate the cross product using the given formula. d. find the magnitude of the resulting vector.
Step-by-step explanation:
To evaluate the expressions given:
a. u dot v: The dot product of two vectors u and v is calculated by multiplying their corresponding components and then adding the products. In this case, if vector u is represented as ui + uj + uk and vector v is represented as vi + vj + vk, then the dot product can be calculated as (ui * vi) + (uj * vj) + (uk * vk).
b. magnitude of u times magnitude of v: The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. For this expression, simply multiply the magnitudes of vectors u and v.
c. u cross v: The cross product of two vectors u and v is calculated using the formula (ui * vj - uj * vi)i - (ui * vk - uk * vi)j + (uj * vk - uk * vj)k.
d. magnitude of u cross v: After calculating the cross product as in part c, take the magnitude of the resulting vector using the square root of the sum of the squares of its components.