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Consider a x b = 41 – 2j + 7k and c = 3i + 4j – k.

Find the indicated scalar or vector.
a · (b × c)

1 Answer

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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.

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