If a⃗ = 2î + 3ĵ - k̂, b⃗ = -î + 2ĵ - 4k̂, c⃗ = î + ĵ + k̂, then (a⃗ × b⃗) · (a⃗ × c⃗) is:

If $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$, $\vec{b} = -\hat{i} + 2\hat{j} - 4\hat{k}$, $\vec{c} = \hat{i} + \hat{j} + \hat{k}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{a} \times \vec{c})$ is:

a60
b64
c74
d-74

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Answer

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Correct option: d

Answer: (d) $-74$ $\vec{a}\times\vec{b} = -10\hat{i} + 9\hat{j} + 7\hat{k}$ and $\vec{a}\times\vec{c} = 4\hat{i} - 3\hat{j} - \hat{k}$, so the dot product is $-40 - 27 - 7 = -74$.