Final answer:
To find a · (b × c), we need to calculate the cross product of b and c, and then find the dot product of a with the resulting vector. The indicated scalar or vector is -8.
Step-by-step explanation:
To find the scalar or vector of a · (b × c), we need to first calculate the cross product of vectors b and c, and then find the dot product of vector a with the resulting vector. Let's perform the calculations:
Step 1: Cross product of b and c:
b × c = (41 – 2j + 7k) × (3i + 4j – k)
Using the rules of cross product, we can expand this expression as:
b × c = (2 × (-k) - 7 × 4j)i + (41 × (-k) - 3 × (-k))j + (3 × 4j - 41 × 7)i
b × c = -8i + 164j + 5k
Step 2: Dot product of a with b × c:
a · (b × c) = (1 × (-8) + 0 × 164 + 0 × 5)
a · (b × c) = -8
Therefore, the indicated scalar or vector is -8.