Find 𝐚⋅(𝐛 × 𝐜), if 𝐚 = 2𝑖 + 𝑗 + 3𝑘, 𝐛 = −𝑖 + 2𝑗 + 𝑘, and 𝐜 = 3𝑖 + 𝑗 + 2𝑘.

(𝐛 × 𝐜) = (−𝑖 + 2𝑗 + 𝑘) × (3𝑖 + 𝑗 + 2𝑘), which implies (𝐛 × 𝐜) = (4)𝑖 + (3 + 2)𝑗 + (−1 − 6)𝑘 = 3𝑖 + 5𝑗 − 7𝑘

𝐚 ⋅ (𝐛 × 𝐜) = (2𝑖 + 𝑗 + 3𝑘) ⋅ (3𝑖 + 5𝑗 − 7𝑘) = 6 + 5 − 21 = −10.