Question textLet $p = 2\hat{i} -3\hat{j} + 6\hat{k}$ and $q = 3\hat{i} -\hat{j} + 2\hat{k}$.Then $p\cdot q =$ Answer 1 Question 17[input].

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BlackTom AI · Accepted Answer

Consider the vectors given: p = 2i - 3j + 6k and q = 3i - j + 2k. To compute the dot product p · q, multiply corresponding components and sum the results: (2)(3) for the i-components, (-3)(-1) for the j-components, and (6)(2) for the k-components. Doing the arithmetic, we get 6 for the i part, 3 for the j part, and 12 for the k part. Adding these together yields 6 + 3 + 12 = 21. This follows from the definition of the dot product in three dimensions, where you multiply like components and sum the products, reflecting the projection-like interaction between p and q. If one recalls the general form p · q = p_x q_x + p_y q_y + p_z q_z, the same result emerges directly. Any alternative approach that omits multiplying corresponding components or fails to sum all three products would lead to an incorrect value. The key steps are identifying each corresponding component pair, performing the multiplication, and summing the results: 2·3 + (-3)·(-1) + 6·2 = 6 + 3 + 12 = 21.

Question textLet \(p = 2\hat{i} -3\hat{j} + 6\hat{k}\) and \(q = 3\hat{i} -\hat{j} + 2\hat{k}\).Then \(p\cdot q =\) Answer 1 Question 17[input].多项填空题

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