Final answer:
To find A.(A × B), you need to calculate A × B (A cross B) and then take the dot product of A with the result. The dot product is -66.
Step-by-step explanation:
To find A.(A × B), we first need to calculate A × B (A cross B) and then take the dot product of A with the result.
A × B = (-5i + 6j - 3k) × (3i + 4j + 2k)
= (-5 * 3) î × î + (-5 * 4) î × ĵ + (-5 * 2) î × k + (6 * 3) ĵ × î + (6 * 4) ĵ × ĵ + (6 * 2) ĵ × k + (-3 * 3) k × î + (-3 * 4) k × ĵ + (-3 * 2) k × k
= 0 +0 +0 + 18k - 24k + 0 + -9j + 0 + 6i
= 6i - 9j - 6k
A.(A × B) = (-5i + 6j - 3k) . (6i - 9j - 6k)
= (-5 * 6) + (6 * -9) + (-3 * -6)
= -30 -54 +18
= -66